Contents

1 Spectrometer 1 1.1 Optical spectrometer ...... 1 1.2 Mass spectrometer ...... 1 1.3 Time-of-flight spectrometer ...... 1 1.4 Magnetic spectrometer ...... 1 1.5 Resolution ...... 2 1.6 References ...... 2

2 Prism 3 2.1 How prisms work ...... 3 2.1.1 Deviation angle and dispersion ...... 4 2.2 Prisms and the nature of light ...... 4 2.3 Types of prisms ...... 5 2.3.1 Dispersive prisms ...... 5 2.3.2 Reflective prisms ...... 5 2.3.3 Polarizing prisms ...... 5 2.3.4 Deflecting prisms ...... 6 2.4 In optometry ...... 6 2.5 See also ...... 6 2.6 References ...... 6 2.7 Further reading ...... 6 2.8 External links ...... 6

3 Minimum deviation 7 3.1 References ...... 7

4 Angle of incidence 8 4.1 Optics ...... 8 4.1.1 Grazing angle ...... 8 4.2 Angle of incidence of fixed-wing aircraft ...... 8 4.3 See also ...... 9 4.4 Notes ...... 9 4.5 External links ...... 9

i ii CONTENTS

5 Refractive index 10 5.1 Definition ...... 10 5.2 History ...... 11 5.3 Typical values ...... 11 5.3.1 Refractive index below unity ...... 11 5.3.2 Negative refractive index ...... 12 5.4 Microscopic explanation ...... 12 5.5 Dispersion ...... 12 5.6 Complex refractive index ...... 13 5.7 Relations to other quantities ...... 14 5.7.1 Optical path length ...... 14 5.7.2 Refraction ...... 15 5.7.3 Total internal reflection ...... 15 5.7.4 Reflectivity ...... 15 5.7.5 Lenses ...... 15 5.7.6 Microscope resolution ...... 16 5.7.7 Relative permittivity and permeability ...... 16 5.7.8 Density ...... 16 5.7.9 Group index ...... 17 5.7.10 Momentum (Abraham–Minkowski controversy) ...... 17 5.7.11 Other relations ...... 17 5.7.12 Refractivity ...... 17 5.8 Nonscalar, nonlinear, or nonhomogeneous refraction ...... 17 5.8.1 Birefringence ...... 17 5.8.2 Nonlinearity ...... 18 5.8.3 Inhomogeneity ...... 18 5.9 Refractive index measurement ...... 18 5.9.1 Homogeneous media ...... 19 5.9.2 Refractive index variations ...... 19 5.10 Applications ...... 20 5.11 See also ...... 20 5.12 References ...... 20 5.13 External links ...... 22

6 Prism spectrometer 23 6.1 Theory ...... 23 6.2 Usage ...... 23 6.2.1 Spectroscopy ...... 23 6.2.2 Measurement of refractive index ...... 23 6.3 External links ...... 24

7 Superprism 25 CONTENTS iii

7.1 See also ...... 25 7.2 References ...... 25 7.3 Further reading ...... 25 7.4 Text and image sources, contributors, and licenses ...... 26 7.4.1 Text ...... 26 7.4.2 Images ...... 27 7.4.3 Content license ...... 28 Chapter 1

Spectrometer

In physics, a spectrometer is an apparatus to measure a spectrum.[1] Generally, a spectrum is a graph that shows intensity as a function of wavelength, of frequency, of B energy, of momentum, or of mass.

v 1.1 Optical spectrometer F + Optical spectrometers (often simply called “spectrome- ters”), in particular, show the intensity of light as a func- tion of wavelength or of frequency. The deflection is pro- duced either by refraction in a prism or by diffraction in a diffraction grating. A positive charged particle moving in a circle under the influence of the Lorentz force F 1.2 Mass spectrometer

A mass spectrometer is an analytical instrument that is used to identify the amount and type of chemicals present in a sample by measuring the mass-to-charge ratio and abundance of gas-phase ions.[2]

1.3 Time-of-flight spectrometer

The energy spectrum of particles of known mass can also be measured by determining the time of flight between Focus of a magnetic semicircular spectrometer two detectors (and hence, the velocity) in a time-of-flight spectrometer. Alternatively, if the velocity is known, masses can be determined in a time-of-flight mass spec- where m and v are mass and velocity of the particle. The trometer. focussing principle of the oldest and simplest magnetic spectrometer, the semicircular spectrometer,[3] invented by J. K. Danisz, is shown on the left. A constant magnetic 1.4 Magnetic spectrometer field is perpendicular to the page. Charged particles of momentum p that pass the slit are deflected into circular paths of radius r = p/qB. Evidently, they hit the horizontal When a fast charged particle (charge q, mass m) enters line at nearly the same place, the focus, where a particle a constant magnetic field B at right angles, it is deflected counter should be placed. Varying B, this makes possi- into a circular path of radius r, due to the Lorentz force. ble to measure the energy spectrum of alpha particles in The momentum p of the particle is then given by an alpha particle spectrometer, of beta particles in a beta particle spectrometer,[1] of particles (e.g., fast ions) in a particle spectrometer, or to measure the relative content p = mv = qBr of the various masses in a mass spectrometer.

1 2 CHAPTER 1. SPECTROMETER

Since Danysz' time, many types of magnetic spectrom- eters more complicated than the semicircular type have been devised.[1]

1.5 Resolution

Generally, the resolution of an instrument tells us how well two close-lying energies (or wavelengths, or frequen- cies, or masses) can be resolved. Generally, for an instru- ment with mechanical slits, higher resolution will mean lower intensity.[1]

1.6 References

[1] K. Siegbahn, Alpha-, Beta- and Gamma-Ray Spec- troscopy, North-Holland Publishing Co. Amsterdam (1966)

[2] “mass spectrometer” (PDF). 2009. doi:10.1351/goldbook.M03732.

[3] Jan Kazimierz Danysz, Le Radium 9, 1 (1912); 10, 4 (1913) Chapter 2

Prism

This article is about a prism in optics. For a prism in ge- light into components with different polarizations. ometry, see Prism (geometry). For other uses, see Prism (disambiguation). “Prismatic” redirects here. For other uses, see Prismatic 2.1 How prisms work (disambiguation). In optics, a prism is a transparent optical element with

A triangular prism, dispersing light; waves shown to illustrate the differing wavelengths of light. (Click to view animation)

Light changes speed as it moves from one medium to an- other (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light’s path de- pends on the angle that the incident beam of light makes A plastic prism with the surface, and on the ratio between the refractive indices of the two media (Snell’s law). The refractive flat, polished surfaces that refract light. At least two of index of many materials (such as glass) varies with the the flat surfaces must have an angle between them. The wavelength or color of the light used, a phenomenon exact angles between the surfaces depend on the appli- known as dispersion. This causes light of different col- cation. The traditional geometrical shape is that of a ors to be refracted differently and to leave the prism at triangular prism with a triangular base and rectangular different angles, creating an effect similar to a rainbow. sides, and in colloquial use “prism” usually refers to this This can be used to separate a beam of white light into type. Some types of optical prism are not in fact in the its constituent spectrum of colors. Prisms will generally shape of geometric prisms. Prisms can be made from any disperse light over a much larger frequency bandwidth material that is transparent to the wavelengths for which than diffraction gratings, making them useful for broad- they are designed. Typical materials include glass, plastic spectrum spectroscopy. Furthermore, prisms do not suf- and fluorite. fer from complications arising from overlapping spectral A dispersive prism can be used to break light up into its orders, which all gratings have. constituent spectral colors (the colors of the rainbow). Prisms are sometimes used for the internal reflection at Furthermore, prisms can be used to reflect light, or to split the surfaces rather than for dispersion. If light inside the

3 4 CHAPTER 2. PRISM

prism hits one of the surfaces at a sufficiently steep an- 2.2 Prisms and the nature of light gle, total internal reflection occurs and all of the light is reflected. This makes a prism a useful substitute for a mirror in some situations.

2.1.1 Deviation angle and dispersion

α ʹ θ0 ʹ θ1 θ θ0 1 θ2

0 1 2

A ray trace through a prism with apex angle α. Regions 0, 1, and 2 have indices of refraction n0 , n1 , and n2 , and primed angles θ′ indicate the ray’s angle after refraction.

Ray angle deviation and dispersion through a prism can be determined by tracing a sample ray through the ele- ment and using Snell’s law at each interface. For the prism shown at right, the indicated angles are given by A triangular prism, dispersing light

Before Isaac Newton, it was believed that white light was ( ) ′ n0 colorless, and that the prism itself produced the color. θ0 = arcsin sin θ0 n1 Newton’s experiments demonstrated that all the colors al- ′ ready existed in the light in a heterogeneous fashion, and θ1 = α − θ 0( ) that “corpuscles” (particles) of light were fanned out be- ′ n1 θ = arcsin sin θ cause particles with different colors traveled with differ- 1 n 1 2 ent speeds through the prism. It was only later that Young ′ − θ2 = θ1 α and Fresnel combined Newton’s particle theory with Huy- gens’ wave theory to show that color is the visible mani- All angles are positive in the direction shown in the image. festation of light’s wavelength. For a prism in air n0 = n2 ≃ 1 . Defining n = n1 , the deviation angle δ is given by Newton arrived at his conclusion by passing the red color from one prism through a second prism and found the color unchanged. From this, he concluded that the colors ( [ ( )]) 1 must already be present in the incoming light — thus, the δ = θ +θ = θ +arcsin n sin α−arcsin sin θ −α 0 2 0 n 0 prism did not create colors, but merely separated colors that are already there. He also used a lens and a sec- If the angle of incidence θ0 and prism apex angle α are ond prism to recompose the spectrum back into white ≈ ≈ both small, sin θ θ and arcsinx x if the angles are light. This experiment has become a classic example of expressed in radians. This allows the nonlinear equation the methodology introduced during the scientific revolu- in the deviation angle δ to be approximated by tion. The results of this experiment dramatically trans- formed the field of metaphysics, leading to John Locke's ( [( )]) primary vs secondary quality distinction. 1 δ ≈ θ −α+ n α− θ = θ −α+nα−θ = (n−1)α . 0 n 0 0 0 Newton discussed prism dispersion in great detail in his book Opticks.[1] He also introduced the use of more The deviation angle depends on wavelength through n, so than one prism to control dispersion.[2] Newton’s descrip- for a thin prism the deviation angle varies with wavelength tion of his experiments on prism dispersion was quali- according to tative, and is quite readable. A quantitative description of multiple-prism dispersion was not needed until mul- tiple prism laser beam expanders were introduced in the δ(λ) ≈ [n(λ) − 1]α 1980s.[3] 2.3. TYPES OF PRISMS 5

2.3 Types of prisms 2.3.2 Reflective prisms

2.3.1 Dispersive prisms Reflective prisms are used to reflect light, in order to flip, invert, rotate, deviate or displace the light beam. They are typically used to erect the image in binoculars or single- lens reflex cameras – without the prisms the image would be upside down for the user. Many reflective prisms use total internal reflection to achieve high reflectivity. The most common reflective prisms are:

• Porro prism

• Porro–Abbe prism

• Amici roof prism

• Pentaprism and roof pentaprism

• Abbe–Koenig prism

• Schmidt–Pechan prism 1 • Bauernfeind prism

• Dove prism

• Retroreflector prism 2 Beam-splitting prisms Some reflective prisms are used for splitting a beam into two or more beams:

Comparison of the spectra obtained from a diffraction grating • by diffraction (1), and a prism by refraction (2). Longer wave- Beam splitter cube lengths (red) are diffracted more, but refracted less than shorter • wavelengths (violet). Dichroic prism

Main article: Dispersive prism 2.3.3 Polarizing prisms

Dispersive prisms are used to break up light into its con- There are also polarizing prisms which can split a beam stituent spectral colors because the refractive index de- of light into components of varying polarization. These pends on frequency; the white light entering the prism is a are typically made of a birefringent crystalline material. mixture of different frequencies, each of which gets bent slightly differently. Blue light is slowed down more than • Nicol prism red light and will therefore be bent more than red light. • Wollaston prism • Triangular prism • Nomarski prism – a variant of the Wollaston prism • Abbe prism with advantages in microscopy • Rochon prism • Pellin–Broca prism • Sénarmont prism • Amici prism • Glan–Foucault prism • Compound prism • Glan–Taylor prism • Grism, a dispersive prism with a diffraction grating on its surface • Glan–Thompson prism 6 CHAPTER 2. PRISM

2.3.4 Deflecting prisms 2.6 References

Wedge prisms are used to deflect a beam of light by a fixed [1] I. Newton (1704). Opticks. London: Royal Society. ISBN angle. A pair of such prisms can be used for beam steer- 0-486-60205-2. ing; by rotating the prisms the beam can be deflected into any desired angle within a conical “field of regard”. The [2] “The Discovery of the Spectrum of Light”. Retrieved 19 December 2009. most commonly found implementation is a Risley prism [4] pair. Two wedge prisms can also be used as an anamor- [3] F. J. Duarte and J. A. Piper (1982). “Dispersion phic pair to change the shape of a beam. This is used to theory of multiple-prism beam expanders for pulsed make a round beam from the elliptical output of a laser dye lasers”. Opt. Commun. 43 (5): 303– diode. 307. Bibcode:1982OptCo..43..303D. doi:10.1016/0030- 4018(82)90216-4. Rhomboid prisms are used to laterally displace a beam of light without inverting the image. [4] B.D. Duncan; et al. (2003). “Wide-angle achro- matic prism beam steering for infrared coun- Deck prisms were used on sailing ships to bring daylight termeasure applications”. Opt. Eng. 42 (4): below deck, since candles and kerosene lamps are a fire 1038–1047. Bibcode:2003OptEn..42.1038D. hazard on wooden ships. doi:10.1117/1.1556393.

[5] Kaplan, M; Carmody, D. P.; Gaydos, A (1996). “Postural 2.4 In optometry orientation modifications in autism in response to ambient lenses”. Child Psychiatry and Human Development 27 (2): 81–91. PMID 8936794. By shifting corrective lenses off axis, images seen through them can be displaced in the same way that a prism dis- places images. Eye care professionals use prisms, as well 2.7 Further reading as lenses off axis, to treat various orthoptics problems: • • Diplopia (double vision) Hecht, Eugene (2001). Optics (4th ed.). Pearson Education. ISBN 0-8053-8566-5. • Positive and negative fusion problems • Positive relative accommodation and negative rela- tive accommodation problems. 2.8 External links

Prism spectacles with a single prism perform a relative • Java applet of refraction through a prism displacement of the two eyes, thereby correcting eso-, exo, hyper- or hypotropia. In contrast, spectacles with prisms of equal power for both eyes, called yoked prisms (also: conjugate prisms, ambient lenses or performance glasses) shift the visual field of both eyes to the same extent.[5]

2.5 See also

• Minimum deviation • Multiple-prism dispersion theory • Prism compressor • Prism dioptre • Prism spectrometer • Prism (geometry) • Theory of Colours • Triangular prism (geometry) • Superprism • Eyeglass prescription Chapter 3

Minimum deviation

prism or water drop is deflected twice: once entering, and again when exiting. The sum of these two deflections is called the deviation angle. The deviation angle in a prism depends upon: Refractive index of the prism: The refractive index de- pends on the material and the wavelength of the light. The larger the refractive index, the larger the deviation angle. Angle of the prism: The larger the prism angle, the Light is deflected as it enters a material with refractive index > 1. larger the deviation angle. Angle of incidence: The deviation angle depends on the angle that the beam enters the object, called angle of inci- dence. The deviation angle first decreases with increasing incidence angle, and then it increases. There is an angle of incidence at which the sum of the two deflections is a minimum. The deviation angle at this point is called the “minimum deviation” angle, or “angle of minimum deviation”.[1] At the minimum deviation an- gle, the incidence and exit angles of the ray are identical. This is a consequence of the principle of time reversibil- ity; if the incidence and exit angles were not identical, then reversing the paths (exit becomes entrance, and vice versa) would indicate erroneously that there were two in- A ray of light is deflected twice in a prism. The sum of these cidence angles resulting in minimum deviation. One of deflections is the deviation angle. the factors that causes a rainbow is the bunching of light rays at the minimum deviation angle that is close to the rainbow angle. A convenient way to measure the refractive index of a prism is to direct a light ray through the prism so it pro- duces the minimum deviation angle. This yields a simple formula:[2]

A+Dλ sin( 2 ) nλ = A sin( 2 ) where n is the refractive index at a wavelength λ , D is the angle of minimum deviation, and A is the internal angle of the prism. When the entrance and exit angles are equal, the deviation angle of a ray passing through a prism will be a minimum. 3.1 References As a ray of light enters a transparent material, the ray’s direction is deflected, based on both the entrance angle [1] Mark A. Peterson. “Minimum Deviation by a Prism”. (typically measured relative to the perpendicular to the Mount Holyoke College. surface) and the material’s refractive index, and according to Snell’s Law. A beam passing through an object like a [2] “Derivation of Angle of Deviation through a Prism”.

7 Chapter 4

Angle of incidence

for nearly 50 years until a closed-form result was derived by mathematicians Allen R Miller and Emanuel Vegh in 1991.[1]

Air Total internal Critical angle θ2 reflection n2 Refracted ray

n1 θc θ1 θ2 Incidentθ ray1 Water

Refraction of light at the interface between two media.

4.1.1 Grazing angle Angle of incidence When dealing with a beam that is nearly parallel to a sur- face, it is sometimes more useful to refer to the angle be- Angle of incidence is a measure of deviation of some- tween the beam and the surface, rather than that between thing from “straight on”, for example: the beam and the surface normal, in other words 90° mi- nus the angle of incidence. This small angle is called a • in the approach of a ray to a surface, or glancing angle or grazing angle. Incidence at grazing angles is called “grazing incidence”. • the angle at which the wing or horizontal tail of an airplane is installed on the fuselage, measured rela- Grazing incidence diffraction is used in X-ray spec- tive to the axis of the fuselage. troscopy and atom optics, where significant reflection can be achieved only at small values of the grazing angle. Ridged mirrors are designed for reflection of atoms com- ing at small grazing angle. This angle is usually measured 4.1 Optics in milliradians. In optics, there is Lloyd’s mirror.

In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpen- 4.2 Angle of incidence of fixed- dicular to the surface at the point of incidence, called the normal. The ray can be formed by any wave: optical, wing aircraft acoustic, microwave, X-ray and so on. In the figure above, the red line representing a ray makes an angle θ with the On fixed-wing aircraft, the angle of incidence (sometimes normal (dotted line). The angle of incidence at which referred to as the mounting angle[2]) is the angle between light is first totally internally reflected is known as the the chord line of the wing where the wing is mounted to critical angle. The angle of reflection and angle of re- the fuselage, and a reference axis along the fuselage (often fraction are other angles related to beams. the direction of minimum drag, or where applicable, the Determining the angle of reflection with respect to a pla- longitudinal axis). The angle of incidence is fixed in the nar surface is trivial, but the computation for almost any design of the aircraft, and with rare exceptions, cannot be other surface is significantly more difficult. The exact so- varied in flight. lution for a sphere (which has important applications in The term can also be applied to horizontal surfaces in gen- astronomy and computer graphics) was an open problem eral (such as canards or horizontal stabilizers) for the an-

8 4.5. EXTERNAL LINKS 9

[3] Kermode, A.C. (1972), Mechanics of Flight, Chapter 3, 8th edition, Pitman Publishing, London. ISBN 0-273- 31623-0

4.5 External links

• Weisstein, Eric W., “Angle of incidence”, MathWorld.

• geometry : rebound on the strip billiards Flash ani- mation Angle of incidence of an airplane wing on an airplane.

gle they make relative the longitudinal axis of the fuse- lage. The figure to the right shows a side view of an airplane. The extended chord line of the wing root (red line) makes an angle with the longitudinal axis (roll axis) of the air- craft (blue line). Wings are typically mounted at a small positive angle of incidence, to allow the fuselage to be have a low angle with the airflow in cruising flight. An- gles of incidence of about 6° are common on most general aviation designs. Other terms for angle of incidence in this context are rigging angle and rigger’s angle of inci- dence. It should not be confused with the angle of attack, which is the angle the wing chord presents to the airflow in flight. Note that some ambiguity in this terminology exists, as some engineering texts that focus solely on the study of airfoils and their medium may use either term when referring to angle of attack. The use of the term “angle of incidence” to refer to the angle of attack occurs chiefly in British usage.[3]

4.3 See also

• Effect of sun angle on climate

• Reflection (physics)

• Refraction

• Season

• Total internal reflection

4.4 Notes

[1] Allen R Miller and Emanuel Vegh (1993). “Ex- act Result for the Grazing Angle of Specular Reflec- tion from a Sphere”. SIAM Review 35: 472–480. doi:10.1137/1035091.

[2] Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. ISBN 978-0-470-53975-0. Chapter 5

Refractive index

torically first use of refractive indices and is described by Snell’s law of refraction, n1 sin θ1 = n2 sin θ2, where θ1 and θ2 are the angles of incidence and refraction, respec- tively, of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster’s angle.[1] The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the phase velocity of light in a medium is v = c/n, and similarly the wavelength A ray of light being refracted in a plastic block. in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum. This implies that vacuum has a In optics the refractive index or index of refraction refractive index of 1, and that the frequency (f = v/λ) of n of an optical medium is a dimensionless number that the wave is not affected by the refractive index. describes how light, or any other radiation, propagates The refractive index varies with the wavelength of light. through that medium. It is defined as This is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, c and chromatic aberration in lenses. Light propagation in n = , v absorbing materials can be described using a complex- valued refractive index.[2] The imaginary part then han- where c is the speed of light in vacuum and v is the phase dles the attenuation, while the real part accounts for re- velocity of light in the medium. fraction. The concept of refractive index is widely used within refractive index the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as n1 n2 sound. In this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen.[3] normal θ2

θ1 5.1 Definition

The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, and the phase velocity v of light in the medium,[1] interface c n = . Refraction of a light ray. v The refractive index determines how much light is bent, The phase velocity is the speed at which the crests or the or refracted, when entering a material. This is the his- phase of the wave moves, which may be different from

10 5.3. TYPICAL VALUES 11 the group velocity, the speed at which the pulse of light 5.3 Typical values or the envelope of the wave moves. The definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used.[1] Historically air at a standardized pressure and temperature have been common as a reference medium.

5.2 History

Diamonds have a very high refractive index of 2.42.

See also: List of refractive indices

For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the table to the right. These values are measured at the yellow doublet sodium D-line, with a wavelength of 589 nanometers, as is conventionally done.[11] Gases at atmo- spheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, with aerogel as the clear ex- ception. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265.[12] Diamond lies at the other end of the range with a refractive index as high as 2.42. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.[13] For infrared light refractive indices can be considerably Thomas Young coined the term index of refraction. higher. Germanium is transparent in the wavelength re- gion from 2 to 14 µm and has a refractive index of about 4, making it an important material for infrared optics.[14] Thomas Young was presumably the person who first used, and invented, the name “index of refraction”, in 1807.[4] At the same time he changed this value of refractive 5.3.1 Refractive index below unity power into a single number, instead of the traditional ra- tio of two numbers. The ratio had the disadvantage of According to the theory of relativity, no information can different appearances. Newton, who called it the “pro- travel faster than the speed of light in vacuum, but this portion of the sines of incidence and refraction”, wrote it does not mean that the refractive index cannot be lower as a ratio of two numbers, like “529 to 396” (or “nearly [5] than 1. The refractive index measures the phase velocity 4 to 3"; for water). Hauksbee, who called it the “ratio of light, which does not carry information.[15] The phase of refraction”, wrote it as a ratio with a fixed numerator, velocity is the speed at which the crests of the wave move like “10000 to 7451.9” (for urine).[6] Hutton wrote it as a [7] and can be faster than the speed of light in vacuum, and ratio with a fixed denominator, like 1.3358 to 1 (water). thereby give a refractive index below 1. This can occur Young did not use a symbol for the index of refraction, close to resonance frequencies, for absorbing media, in in 1807. In the next years, others started using differ- plasmas, and for X-rays. In the X-ray regime the refrac- ent symbols: n, m, and µ.[8][9][10] The symbol n gradually tive indices are lower than but very close to 1 (exceptions prevailed. close to some resonance frequencies).[16] As an exam- 12 CHAPTER 5. REFRACTIVE INDEX ple, water has a refractive index of 0.99999974 = 1 − radiated in other directions or even at other frequencies 2.6×10−7 for X-ray radiation at a photon energy of 30 (see scattering). [16] keV (0.04 nm wavelength). Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there 5.3.2 Negative refractive index are several possibilities:

See also: Negative index metamaterials • If the electrons emit a light wave which is 90° out Recent research has also demonstrated the existence of of phase with the light wave shaking them, it will cause the total light wave to travel more slowly. This is called “normal refraction”, is observed for trans- parent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.[19]

• If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the total light wave to travel more quickly. This is called “anomalous refraction”, and is observed close to absorption lines, with X-rays, and in some mi- crowave systems. It corresponds to a refractive in- dex less than 1. (Even though the phase velocity of light is greater than the speed of light in vacuum c, the signal velocity is not, as discussed above.) If the response is sufficiently strong and out-of-phase, the A split-ring resonator array arranged to produce a negative index [19] of refraction for microwaves. result is a negative refractive index. • If the electrons emit a light wave which is 180° out materials with a negative refractive index, which can oc- of phase with the light wave shaking them, it will de- cur if permittivity and permeability have simultaneous structively interfere with the original light to reduce negative values.[17] This can be achieved with periodically the total light intensity. This is light absorption in constructed metamaterials. The resulting negative refrac- opaque materials and corresponds to an imaginary tion (i.e., a reversal of Snell’s law) offers the possibility refractive index. of the superlens and other exotic phenomena.[18] • If the electrons emit a light wave which is in phase with the light wave shaking them, it will amplify the 5.4 Microscopic explanation light wave. This is rare, but occurs in lasers due to stimulated emission. It corresponds to an imaginary index of refraction, with the opposite sign to that of At the microscale, an electromagnetic wave’s phase ve- absorption. locity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primar- For most materials at visible-light frequencies, the phase ily the electrons) proportional to the electric susceptibility is somewhere between 90° and 180°, corresponding to a of the medium. (Similarly, the magnetic field creates a combination of both refraction and absorption. disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be “shaken” back and forth at the same frequency.[1]:67 The charges thus radiate their 5.5 Dispersion own electromagnetic wave that is at the same frequency, but usually with a phase delay, as the charges may move Main article: Dispersion (optics) out of phase with the force driving them (see sinusoidally The refractive index of materials varies with the wave- driven harmonic oscillator). The light wave traveling in length (and frequency) of light.[20] This is called disper- the medium is the macroscopic superposition (sum) of all sion and causes prisms and rainbows to divide white light such contributions in the material: the original wave plus into its constituent spectral colors.[21] As the refractive the waves radiated by all the moving charges. This wave index varies with wavelength, so will the refraction an- is typically a wave with the same frequency but shorter gle as light goes from one material to another. Disper- wavelength than the original, leading to a slowing of the sion also causes the focal length of lenses to be wave- wave’s phase velocity. Most of the radiation from oscil- length dependent. This is a type of chromatic aberra- lating material charges will modify the incoming wave, tion, which often needs to be corrected for in imaging changing its velocity. However, some net energy will be systems. In regions of the spectrum where the material 5.6. COMPLEX REFRACTIVE INDEX 13

The variation of refractive index with wavelength for various glasses.

n − 1 V = yellow . nblue − nred For a more accurate description of the wavelength de- pendence of the refractive index, the Sellmeier equation can be used.[22] It is an empirical formula that works well in describing dispersion. Sellmeier coefficients are often Light of different colors has slightly different refractive indices quoted instead of the refractive index in tables. in water and therefore shows up at different positions in the Because of dispersion, it is usually important to specify rainbow. the vacuum wavelength of light for which a refractive in- dex is measured. Typically, measurements are done at various well-defined spectral emission lines; for example, nD usually denotes the refractive index at the Fraunhofer “D” line, the centre of the yellow sodium double emission at 589.29 nm wavelength.[11]

5.6 Complex refractive index

See also: Mathematical descriptions of opacity When light passes through a medium, some part of it will always be attenuated. This can be conveniently taken into account by defining a complex refractive index, In a prism dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors. n = n + iκ.

Here, the real part n is the refractive index and indicates does not absorb light, the refractive index tends to de- the phase velocity, while the imaginary part κ is called crease with increasing wavelength, and thus increase with the “extinction coefficient”—although this can also refer frequency. This is called “normal dispersion”, in contrast to the mass attenuation coefficient—[23]:3 and indicates to “anomalous dispersion”, where the refractive index in- the amount of attenuation when the electromagnetic wave creases with wavelength.[20] For visible light normal dis- propagates through the material.[1]:128 persion means that the refractive index is higher for blue That κ corresponds to attenuation can be seen by inserting light than for red. this refractive index into the expression for electric field of For optics in the visual range, the amount of dispersion of a plane electromagnetic wave traveling in the z-direction. a lens material is often quantified by the Abbe number:[21] We can do this by relating the complex wave number k to 14 CHAPTER 5. REFRACTIVE INDEX

tion significantly, reducing the material’s transparency to these frequencies. The real, n, and imaginary, κ, parts of the complex refrac- tive index are related through the Kramers–Kronig rela- tions. In 1986 A.R. Forouhi and I. Bloomer deduced an equation describing κ as a function of photon energy, E, applicable to amorphous materials. Forouhi and Bloomer then applied the Kramers–Kronig relation to derive the corresponding equation for n as a function of E. The same formalism was applied to crystalline materials by Forouhi and Bloomer in 1988. The refractive index and extinction coefficient, n and κ, cannot be measured directly. They must be deter- mined indirectly from measurable quantities that depend on them, such as reflectance, R, or transmittance, T, or ellipsometric parameters, ψ and δ. The determination of n and κ from such measured quantities will involve de- veloping a theoretical expression for R or T, or ψ and δ in terms of a valid physical model for n and κ. By fitting the theoretical model to the measured R or T, or ψ and δ using regression analysis, n and κ can be deduced. A graduated neutral density filter showing light absorption in the upper half. For X-ray and extreme ultraviolet radiation the complex refractive index deviates only slightly from unity and usu- ally has a real part smaller than 1. It is therefore normally the complex refractive index n through k = 2πn/λ0, with written as n = 1 − δ + iκ (or n = 1 − δ − iκ with the alter- λ0 being the vacuum wavelength; this can be inserted into native convention mentioned above).[2] the plane wave expression as

[ ] [ ] [ ] i(kz−ωt) i(2π(n+iκ)z/λ0−ωt) −2πκz/λ0 i(kz−ωt) E(z, t) = Re E0e = Re E0e 5.7= e RelationsRe E0e to other. quantities

Here we see that κ gives an exponential decay, as ex- pected from the Beer–Lambert law. Since intensity is 5.7.1 Optical path length proportional to the square of the electric field, it will de- pend on the depth into the material as exp(−4πκz/λ0), [1]:128 and the attenuation coefficient becomes α = 4πκ/λ0. This also relates it to the penetration depth, the distance after which the intensity is reduced by 1/e, δ = 1/α = λ0/(4πκ). Both n and κ are dependent on the frequency. In most cir- cumstances κ > 0 (light is absorbed) or κ = 0 (light travels forever without loss). In special situations, especially in the gain medium of lasers, it is also possible that κ < 0, corresponding to an amplification of the light. An alternative convention uses n = n − iκ instead of n = n + iκ, but where κ > 0 still corresponds to loss. Therefore these two conventions are inconsistent and should not be confused. The difference is related to defining sinusoidal time dependence as Re[exp(−iωt)] versus Re[exp(+iωt)]. The colors of a soap bubble are determined by the optical path See Mathematical descriptions of opacity. length through the thin soap film in a phenomenon called thin- Dielectric loss and non-zero DC conductivity in materi- film interference. als cause absorption. Good dielectric materials such as glass have extremely low DC conductivity, and at low Optical path length (OPL) is the product of the geometric frequencies the dielectric loss is also negligible, resulting length d of the path light follows through a system, and in almost no absorption. However, at higher frequencies the index of refraction of the medium through which it (such as visible light), dielectric loss may increase absorp- propagates,[24] 5.7. RELATIONS TO OTHER QUANTITIES 15

OPL = nd.

This is an important concept in optics because it deter- mines the phase of the light and governs interference and diffraction of light as it propagates. According to Fermat’s principle, light rays can be characterized as those curves that optimize the optical path length.[1]:68–69

5.7.2 Refraction

P n n index 1 2 Total internal reflection can be seen at the air-water boundary. v1 v2 velocity θ1 normal going to a less optically dense material, i.e., one with lower refractive index. To get total internal reflection the O θ2 angles of incidence θ1 must be larger than the critical angle[27] Q

interface ( ) n2 Refraction of light at the interface between two media of different θc = arcsin . n1 refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index 5.7.4 Reflectivity medium is closer to the normal. Apart from the transmitted light there is also a reflected When light moves from one medium to another, it part. The reflection angle is equal to the incidence angle, changes direction, i.e. it is refracted. If it moves from and the amount of light that is reflected is determined by a medium with refractive index n1 to one with refractive the reflectivity of the surface. The reflectivity can be cal- index n , with an incidence angle to the surface normal of 2 culated from the refractive index and the incidence angle θ , the refraction angle θ can be calculated from Snell’s 1 2 with the Fresnel equations, which for normal incidence law:[25] reduces to[26]:44

n1 sin θ1 = n2 sin θ2. − 2 n1 n2 R0 = . When light enters a material with higher refractive index, n1 + n2 the angle of refraction will be smaller than the angle of in- For common glass in air, n1 = 1 and n2 = 1.5, and thus cidence and the light will be refracted towards the normal about 4% of the incident power is reflected.[28] At other of the surface. The higher the refractive index, the closer incidence angles the reflectivity will also depend on the to the normal direction the light will travel. When pass- polarization of the incoming light. At a certain angle ing into a medium with lower refractive index, the light called Brewster’s angle, p-polarized light (light with the will instead be refracted away from the normal, towards electric field in the plane of incidence) will be totally the surface. transmitted. Brewster’s angle can be calculated from the two refractive indices of the interface as [1]:245 5.7.3 Total internal reflection ( ) n2 If there is no angle θ2 fulfilling Snell’s law, i.e., θB = arctan . n1

n1 sin θ1 > 1, 5.7.5 Lenses n2 the light cannot be transmitted and will instead undergo The focal length of a lens is determined by its refrac- [26]:49–50 total internal reflection. This occurs only when tive index n and the radii of curvature R1 and R2 of its 16 CHAPTER 5. REFRACTIVE INDEX

and the complex refractive index n, with real and imagi- nary parts n and κ (the latter called the “extinction coef- ficient”), follow the relation

2 2 εr = εr + iε˜r = n = (n + iκ) , and their components are related by:[33]

2 2 εr = n − κ , The power of a magnifying glass is determined by the shape and ε˜r = 2nκ, refractive index of the lens. and:

surfaces. The power of a thin lens in air is given by the √ [29] Lensmaker’s formula: |ε | + εr n = r , 2 √ ( ) |ε | − ε 1 1 1 κ = r r . = (n − 1) − , 2 f R1 R2 √ | | 2 2 where εr = εr +ε ˜r is the complex modulus. where f is the focal length of the lens. 5.7.8 Density 5.7.6 Microscope resolution

The resolution of a good optical microscope is mainly de- termined by the numerical aperture (NA) of its objective lens. The numerical aperture in turn is determined by the refractive index n of the medium filling the space between the sample and the lens and the half collection angle of light θ according to[30]:6

NA = n sin θ.

For this reason oil immersion is commonly used to ob- tain high resolution in microscopy. In this technique the objective is dipped into a drop of high refractive index [30]:14 Relation between the refractive index and the density of silicate immersion oil on the sample under study. and borosilicate glasses.[34]

In general, the refractive index of a glass increases with 5.7.7 Relative permittivity and permeabil- its density. However, there does not exist an overall lin- ity ear relation between the refractive index and the density for all silicate and borosilicate glasses. A relatively high The refractive index of electromagnetic radiation equals refractive index and low density can be obtained with glasses containing light metal oxides such as Li2O and √ MgO, while the opposite trend is observed with glasses n = εrµr, containing PbO and BaO as seen in the diagram at the right. where εᵣ is the material’s relative permittivity, and μᵣ is its relative permeability.[31]:229 The refractive index Many oils (such as olive oil) and ethyl alcohol are exam- is used for optics in Fresnel equations and Snell’s law; ples of liquids which are more refractive, but less dense, while the relative permittivity and permeability are used than water, contrary to the general correlation between in Maxwell’s equations and electronics. Most naturally density and refractive index. occurring materials are non-magnetic at optical frequen- For gases, n − 1 is proportional to the density of the gas cies, that is μr is very close to 1, [32] therefore n is approx- as long as the chemical composition does not change.[35] imately √εᵣ. In this particular case, the complex relative This means that it is also proportional to the pressure and permittivity εᵣ, with real and imaginary parts εᵣ and ɛ̃ ᵣ, inversely proportional to the temperature for ideal gases. 5.8. NONSCALAR, NONLINEAR, OR NONHOMOGENEOUS REFRACTION 17

5.7.9 Group index A 2010 study suggested that both equations are correct, with the Abraham version being the kinetic momentum Sometimes, a “group velocity refractive index”, usually and the Minkowski version being the canonical momen- called the group index is defined: tum, and claims to explain the contradicting experimental results using this interpretation.[39] c ng = , vg 5.7.11 Other relations where v is the group velocity. This value should not be confused with n, which is always defined with respect As shown in the Fizeau experiment, when light is trans- to the phase velocity. When the dispersion is small, the mitted through a moving medium, its speed relative to a group velocity can be linked to the phase velocity by the stationary observer is: relation[26]:22 ( ) c 1 V = + v 1 − . dv 2 v = v − λ , n n g dλ The refractive index of a substance can be related to its where λ is the wavelength in the medium. In this case polarizability with the Lorentz–Lorenz equation or to the the group index can thus be written in terms of the wave- molar refractivities of its constituents by the Gladstone– length dependence of the refractive index as Dale relation.

n n = . g λ dn 5.7.12 Refractivity 1 + n dλ When the refractive index of a medium is known as a In atmospheric applications, the refractivity is taken as N function of the vacuum wavelength (instead of the wave- = n – 1. Atmospheric refractivity is often expressed as length in the medium), the corresponding expressions for either[40] N = 106(n – 1)[41][42] or N = 108(n – 1)[43] The the group velocity and index are (for all values of disper- multiplication factors are used because the refractive in- [36] sion) dex for air, n deviates from unity by at most a few parts per ten thousand. ( )− dn 1 Molar refractivity, on the other hand, is a measure of the vg = c n − λ0 , total polarizability of a mole of a substance and can be dλ 0 calculated from the refractive index as dn ng = n − λ0 , dλ0 M n2 − 1 where λ0 is the wavelength in vacuum. A = , ρ n2 + 2

5.7.10 Momentum (Abraham–Minkowski where ρ is the density, and M is the molar mass.[26]:93 controversy) Main article: Abraham–Minkowski controversy 5.8 Nonscalar, nonlinear, or non- homogeneous refraction In 1908, Hermann Minkowski calculated the momentum p of a refracted ray as follows:[37] So far, we have assumed that refraction is given by linear equations involving a spatially constant, scalar refractive nE index. These assumptions can break down in different p = , c ways, to be described in the following subsections. where E is energy of the photon, c is the speed of light in vacuum and n is the refractive index of the medium. In 5.8.1 Birefringence 1909, Max Abraham proposed the following formula for this calculation:[38] Main article: Birefringence In some materials the refractive index depends on the [44] E polarization and propagation direction of the light. p = . nc This is called birefringence or optical anisotropy. 18 CHAPTER 5. REFRACTIVE INDEX

scribed by the field of crystal optics, the dielectric constant is a rank-2 tensor (a 3 by 3 matrix). In this case the prop- agation of light cannot simply be described by refractive indices except for polarizations along principal axes.

5.8.2 Nonlinearity

Main article: Nonlinear optics A calcite crystal laid upon a paper with some letters showing double refraction. The strong electric field of high intensity light (such as output of a laser) may cause a medium’s refractive in- dex to vary as the light passes through it, giving rise to nonlinear optics.[1]:502 If the index varies quadratically with the field (linearly with the intensity), it is called the optical Kerr effect and causes phenomena such as self- focusing and self-phase modulation.[1]:264 If the index varies linearly with the field (a nontrivial linear coefficient is only possible in materials that do not possess inversion symmetry), it is known as the Pockels effect.[1]:265

5.8.3 Inhomogeneity

Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity.

In the simplest form, uniaxial birefringence, there is only one special direction in the material. This axis is known as the optical axis of the material.[1]:230 Light with lin- ear polarization perpendicular to this axis will experi- ence an ordinary refractive index nₒ while light polarized in parallel will experience an extraordinary refractive in- dex nₑ.[1]:236 The birefringence of the material is the dif- A gradient-index lens with a parabolic variation of refractive in- ference between these indices of refraction, Δn = nₑ − dex (n) with radial distance (x). The lens focuses light in the nₒ.[1]:237 Light propagating in the direction of the opti- same way as a conventional lens. cal axis will not be affected by the birefringence since the refractive index will be nₒ independent of polariza- If the refractive index of a medium is not constant, but tion. For other propagation directions the light will split varies gradually with position, the material is known as a gradient-index or GRIN medium and is described by into two linearly polarized beams. For light traveling per- [1]:273 pendicularly to the optical axis the beams will have the gradient index optics. Light traveling through such same direction.[1]:233 This can be used to change the po- a medium can be bent or focused, and this effect can be larization direction of linearly polarized light or to con- exploited to produce lenses, some optical fibers and other vert between linear, circular and elliptical polarizations devices. Introducing GRIN elements in the design of an with waveplates.[1]:237 optical system can greatly simplify the system, reducing the number of elements by as much as a third while main- Many crystals are naturally birefringent, but isotropic ma- taining overall performance.[1]:276 The crystalline lens of terials such as plastics and glass can also often be made the human eye is an example of a GRIN lens with a refrac- birefringent by introducing a preferred direction through, tive index varying from about 1.406 in the inner core to e.g., an external force or electric field. This can be uti- approximately 1.386 at the less dense cortex.[1]:203 Some lized in the determination of stresses in structures using common mirages are caused by a spatially varying refrac- photoelasticity. The birefringent material is then placed tive index of air. between crossed polarizers. A change in birefringence will alter the polarization and thereby the fraction of light that is transmitted through the second polarizer. 5.9 Refractive index measurement In the more general case of trirefringent materials de- 5.9. REFRACTIVE INDEX MEASUREMENT 19

5.9.1 Homogeneous media chemical and pharmaceutical industry for process con- trol. Main articles: Refractometry and Refractometer In gemology a different type of refractometer is used The refractive index of liquids or solids can be mea- to measure index of refraction and birefringence of gemstones. The gem is placed on a high refractive in- dex prism and illuminated from below. A high refractive index contact liquid is used to achieve optical contact be- tween the gem and the prism. At small incidence angles most of the light will be transmitted into the gem, but at high angles total internal reflection will occur in the prism. The critical angle is normally measured by look- ing through a telescope.[47]

5.9.2 Refractive index variations

Main article: Phase-contrast imaging The principle of many refractometers. Unstained biological structures appear mostly transpar- sured with refractometers. They typically measure some angle of refraction or the critical angle for total internal reflection. The first laboratory refractometers sold com- mercially were developed by Ernst Abbe in the late 19th century.[45] The same principles are still used today. In this instrument a thin layer of the liquid to be measured is placed between two prisms. Light is shone through the liquid at incidence angles all the way up to 90°, i.e., light rays parallel to the surface. The second prism should have an index of refraction higher than that of the liquid, so that light only enters the prism at angles smaller than the critical angle for total reflection. This angle can then be measured either by looking through a telescope, or with a digital photodetector placed in the focal plane of a lens. The refractive index n of the liquid can then be calculated from the maximum transmission angle θ as n = nG sin θ, where nG is the refractive index of the prism.[46]

A differential interference contrast microscopy image of yeast cells.

ent under Bright-field_microscopy as most cellular struc- tures do not attenuate appreciable quantities of light. Nevertheless, the variation in the materials that consti- tutes these structures also corresponds to a variation in the refractive index. The following techniques convert such variation into measurable amplitude differences: To measure the spatial variation of refractive index in a sample phase-contrast imaging methods are used. These methods measure the variations in phase of the light wave exiting the sample. The phase is proportional to the A handheld refractometer used to measure sugar content of optical path length the light ray has traversed, and thus fruits. gives a measure of the integral of the refractive index along the ray path. The phase cannot be measured di- This type of devices are commonly used in chemical lab- rectly at optical or higher frequencies, and therefore needs oratories for identification of substances and for quality to be converted into intensity by interference with a ref- control. Handheld variants are used in agriculture by, erence beam. In the visual spectrum this is done using e.g., wine makers to determine sugar content in grape Zernike phase-contrast microscopy, differential interfer- juice, and inline process refractometers are used in, e.g., ence contrast microscopy (DIC) or interferometry. 20 CHAPTER 5. REFRACTIVE INDEX

Zernike phase-contrast microscopy introduces a phase • Clausius–Mossotti relation shift to the low spatial frequency components of the image • with a phase-shifting annulus in the Fourier plane of the Ellipsometry sample, so that high-spatial-frequency parts of the im- • Index-matching material age can interfere with the low-frequency reference beam. In DIC the illumination is split up into two beams that • Index ellipsoid are given different polarizations, are phase shifted differ- ently, and are shifted transversely with slightly different • Optical properties of water and ice amounts. After the specimen, the two parts are made to interfere, giving an image of the derivative of the opti- cal path length in the direction of the difference in trans- 5.12 References verse shift.[30] In interferometry the illumination is split up into two beams by a partially reflective mirror. One of [1] Hecht, Eugene (2002). Optics. Addison-Wesley. ISBN the beams is let through the sample before they are com- 0-321-18878-0. bined to interfere and give a direct image of the phase shifts. If the optical path length variations are more than [2] Attwood, David (1999). Soft X-rays and extreme ultravi- a wavelength the image will contain fringes. olet radiation: principles and applications. p. 60. ISBN 0-521-02997-X. There exist several phase-contrast X-ray imaging tech- niques to determine 2D or 3D spatial distribution of re- [3] Kinsler, Lawrence E. (2000). Fundamentals of Acoustics. fractive index of samples in the X-ray regime.[48] John Wiley. p. 136. ISBN 0-471-84789-5.

[4] Young, Thomas (1807). A course of lectures on natural philosophy and the mechanical arts. p. 413. 5.10 Applications [5] Newton, Isaac (1730). Opticks: Or, A Treatise of the Re- flections, Refractions, Inflections and Colours of Light. p. The refractive index is a very important property of the 247. components of any optical instrument that uses refraction. It determines the focusing power of lenses, the dispersive [6] Hauksbee, Francis (1710). “A Description of the Appara- power of prisms, and generally the path of light through tus for Making Experiments on the Refractions of Fluids”. the system. It is the increase in refractive index in the core Philosophical Transactions of the Royal Society of London that guides the light in an optical fiber, and the variations 27 (325–336): 207. doi:10.1098/rstl.1710.0015. in refractive index that reduces the reflectivity of a surface [7] Hutton, Charles (1795). Philosophical and mathematical treated with an anti-reflective coating. dictionary. p. 299.

Since refractive index is a fundamental physical property [8] von Fraunhofer, Joseph (1817). “Bestimmung des of a substance, it is often used to identify a particular sub- Brechungs und Farbenzerstreuungs Vermogens ver- stance, confirm its purity, or measure its concentration. schiedener Glasarten”. Denkschriften der Königlichen Refractive index is used to measure solids, liquids, and Akademie der Wissenschaften zu München 5: 208. Ex- gases. Most commonly it is used to measure the concen- ponent des Brechungsverhältnisses is index of refraction tration of a solute in an aqueous solution. It can also be used as a useful tool to differentiate between different [9] Brewster, David (1815). “On the structure of doubly types of gemstone, due to the unique chatoyance each in- refracting crystals”. Philosophical Magazine 45: 126. doi:10.1080/14786441508638398. dividual stone displays. A refractometer is the instrument used to measure refractive index. For a solution of sugar, [10] Herschel, John F.W. (1828). On the Theory of Light. p. the refractive index can be used to determine the sugar 368. content (see Brix). [11] “Forensic Science Communications, Glass Refractive In- In GPS, the index of refraction is utilized in ray-tracing to dex Determination”. FBI Laboratory Services. Retrieved account for the radio propagation delay due to the Earth’s 2014-09-08. electrically neutral atmosphere. It is also used in Satellite link design for the computation of radiowave attenuation [12] Tabata, M.; et al. (2005). “Development of Silica Aero- in the atmosphere. gel with Any Density” (PDF). 2005 IEEE Nuclear Science Symposium Conference Record.

[13] Naoki Sadayori and Yuji Hotta “Polycarbodiimide having 5.11 See also high index of refraction and production method thereof” US patent 2004/0158021 A1 (2004)

• Fermat’s principle [14] Tosi, Jeffrey L., article on Common Infrared Optical Ma- terials in the Photonics Handbook, accessed on 2014-09- • Calculation of glass properties 10 5.12. REFERENCES 21

[15] Als-Nielsen, J.; McMorrow, D. (2011). Elements of Mod- [30] Carlsson, Kjell (2007). “Light microscopy” (PDF). Re- ern X-ray Physics. Wiley-VCH. p. 25. ISBN 978-0-470- trieved 2015-01-02. 97395-0. One consequence of the real part of n being less than unity is that it implies that the phase velocity inside [31] Bleaney, B.; Bleaney, B.I. (1976). Electricity and Mag- the material, c/n, is larger than the velocity of light, c. This netism (Third ed.). Oxford University Press. ISBN 0-19- does not, however, violate the law of relativity, which re- 851141-8. quires that only signals carrying information do not travel [32] Urzhumov, Yaroslav A.; Urzhumov, Yaroslav A (2005). faster than c. Such signals move with the group velocity, “Electric and magnetic properties of sub-wavelength plas- not with the phase velocity, and it can be shown that the monic crystals”. Journal of Optics A: Pure and Ap- group velocity is in fact less than c. plied Optics 7 (2): S23. Bibcode:2005JOptA...7S..23S. [16] “X-Ray Interactions With Matter”. The Center for X-Ray doi:10.1088/1464-4258/7/2/003. Optics. Retrieved 2011-08-30. [33] Wooten, Frederick (1972). Optical Properties of Solids. [17] Veselago, V. G. (1968). “The electrodynam- New York City: Academic Press. p. 49. ISBN 0-12- ics of substances with simultaneously negative 763450-9.(online pdf) values of ε and μ". Soviet Physics Uspekhi 10 (4): 509–514. Bibcode:1968SvPhU..10..509V. [34] “Calculation of the Refractive Index of Glasses”. Statisti- doi:10.1070/PU1968v010n04ABEH003699. cal Calculation and Development of Glass Properties.

[18] Shalaev, V. M. (2007). “Optical negative-index [35] Stone, Jack A.; Zimmerman, Jay H. (2011-12-28). “Index metamaterials”. Nature Photonics (Nature Publish- of refraction of air”. Engineering metrology toolbox. Na- ing Group) 1: 41–48. Bibcode:2007NaPho...1...41S. tional Institute of Standards and Technology (NIST). Re- doi:10.1038/nphoton.2006.49. Retrieved 2014-09-07. trieved 2014-01-11.

[19] Feynman, Richard P. (2011). Feynman Lectures on [36] Bor, Z.; Osvay, K.; Rácz, B.; Szabó, G. (1990). Physics 1: Mainly Mechanics, Radiation, and Heat. Ba- “Group refractive index measurement by Michelson in- sic Books. ISBN 978-0-465-02493-3. terferometer”. Optics Communications 78 (2): 109– 112. Bibcode:1990OptCo..78..109B. doi:10.1016/0030- [20] R. Paschotta, article on chromatic dispersion in the 4018(90)90104-2. Encyclopedia of Laser Physics and Technology, accessed on 2014-09-08 [37] Minkowski, Hermann (1908). “Die Grundgleichung für die elektromagnetischen Vorgänge in bewegten Körpern”. [21] Carl R. Nave, page on Dispersion in HyperPhysics, De- Nachrichten von der Gesellschaft der Wissenschaften zu partment of Physics and Astronomy, Georgia State Uni- Göttingen, Mathematisch-Physikalische Klasse: 53–111. versity, accessed on 2014-09-08 [38] Abraham, Max (1909). "Zur Elektrodynamik bewegter [22] R. Paschotta, article on Sellmeier formula in the Körper". Rendiconti del Circolo Matematico di Palermo Encyclopedia of Laser Physics and Technology, accessed 28 (1). on 2014-09-08 [39] Barnett, Stephen (2010-02-07). “Resolution of the [23] Dresselhaus, M. S. (1999). “Solid State Physics Part II Abraham-Minkowski Dilemma”. Phys. Rev. Lett. 104 Optical Properties of Solids” (PDF). Course 6.732 Solid (7): 070401. Bibcode:2010PhRvL.104g0401B. State Physics. MIT. Retrieved 2015-01-05. doi:10.1103/PhysRevLett.104.070401. PMID 20366861. [24] R. Paschotta, article on optical thickness in the Encyclopedia of Laser Physics and Technology, accessed [40] Young, A. T. (2011), Refractivity of Air, retrieved 31 July on 2014-09-08 2014

[25] R. Paschotta, article on refraction in the Encyclopedia of [41] Barrell, H.; Sears, J. E. (1939), “The Refraction Laser Physics and Technology, accessed on 2014-09-08 and Dispersion of Air for the Visible Spectrum”, [26] Born, Max; Wolf, Emil (1999). Principles of Optics (7th Philosophical Transactions of the Royal Society of expanded ed.). ISBN 978-0-521-78449-8. London, A, Mathematical and Physical Sciences 238 (786): 1–64, Bibcode:1939RSPTA.238....1B, [27] R. Paschotta, article on [href="https://www.rp-photonics. doi:10.1098/rsta.1939.0004, JSTOR 91351 com/total_internal_reflection.html total internal reflec- tion] in the Encyclopedia of Laser Physics and Technol- [42] Aparicio, Josep M.; Laroche, Stéphane (2011-06- ogy, accessed on 2014-09-08 02). “An evaluation of the expression of the at- mospheric refractivity for GPS signals”. Journal of [28] Swenson, Jim; Incorporates Public Domain material from Geophysical Research (American Geophysical Union) the U.S. Department of Energy (November 10, 2009). 116 (D11): D11104. Bibcode:2011JGRD..11611104A. “Refractive Index of Minerals”. Newton BBS, Argonne doi:10.1029/2010JD015214. Retrieved 13 January 2014. National Laboratory, US DOE. Retrieved 2010-07-28. [43] Ciddor, P. E. (1996), “Refractive Index of Air: New [29] Carl R. Nave, page on the Lens-Maker’s Formula in Equations for the Visible and Near Infrared”, Applied Op- HyperPhysics, Department of Physics and Astronomy, tics 35 (9): 1566–1573, Bibcode:1996ApOpt..35.1566C, Georgia State University, accessed on 2014-09-08 doi:10.1364/ao.35.001566 22 CHAPTER 5. REFRACTIVE INDEX

[44] R. Paschotta, article on birefringence in the Encyclopedia of Laser Physics and Technology, accessed on 2014-09- 09

[45] “The Evolution of the Abbe Refractometer”. Humboldt State University, Richard A. Paselk. 1998. Retrieved 2011-09-03.

[46] “Refractometers and refractometry”. Refractometer.pl. 2011. Retrieved 2011-09-03.

[47] “Refractometer”. The Gemology Project. Retrieved 2011-09-03.

[48] Fitzgerald, Richard (July 2000). “Phase‐Sensitive X‐Ray Imaging”. Physics Today 53 (7): 23. Bibcode:2000PhT....53g..23F. doi:10.1063/1.1292471.

5.13 External links

• NIST calculator for determining the refractive index of air

• Dielectric materials • Science World

• Filmetrics’ online database Free database of refrac- tive index and absorption coefficient information

• RefractiveIndex.INFO Refractive index database featuring online plotting and parameterisation of data • sopra-sa.com Refractive index database as text files (sign-up required) • LUXPOP Thin film and bulk index of refraction and photonics calculations Chapter 6

Prism spectrometer

which in turn is slightly dependent on the wavelength of light that is traveling through it.

6.1 Theory

Light is emitted from a source such as a vapor lamp.A slit selects a thin strip of light which passes through the Setup of a prism spectrometer collimator where it gets parallelized. The aligned light then passes through the prism in which it is refracted twice (once when entering and once when leaving). Due to the nature of a dispersive element the angle with which light is refracted depends on its wavelength. This leads to a spectrum of thin lines of light, each being observable at a different angle. Replacing the prism with a diffraction grating would re- sult in a grating spectrometer. Optical gratings are less expensive, provide much higher resolution, and are eas- ier to calibrate, due to their linear diffraction dependency. A prism’s refraction angle varies nonlinearly with wave- Setup of a prism spectrometer (low angle with light) length. On the other hand, gratings have significant in- tensity losses.

6.2 Usage

6.2.1 Spectroscopy

A prism spectrometer may be used to determine the com- position of a material from its emitted spectral lines.

Setup of a prism spectrometer (high angle with light) 6.2.2 Measurement of refractive index

A prism spectrometer is an optical spectrometer which A prism spectrometer may be used to measure the re- uses a dispersive prism as its dispersive element. The fractive index of a material if the wavelengths of the light prism refracts light into its different colors (wavelengths). used are known. The calibration of a prism spectrometer The dispersion occurs because the angle of refraction is is carried out with known spectral lines from vapor lamps dependent on the refractive index of the prism’s material, or laser light.

23 24 CHAPTER 6. PRISM SPECTROMETER

6.3 External links

• The prism spectrometer Physics Laboratory Guide, Durham University • The Prism Spectrometer

• Spectrometer, Refractive Index of the material of a prism Virtual Laboratory, Amrita University Chapter 7

Superprism

A superprism is a photonic crystal in which an enter- • Nelson B E, Gerken M, Miller D A B, Piestun R, Lin ing beam of light will lead to an extremely large angular C, Harris J S (2000). “Use of a dielectric stack as dispersion. The ability of the photonic crystal to send a one-dimensional photonic crystal for wavelength optical beams with different wavelengths to considerably demultiplexing by beam shifting”. Optics Letters different angles in space in superprisms has been used 25 (20): 1502–4. Bibcode:2000OptL...25.1502N. to demonstrate wavelength demultiplexing in these struc- doi:10.1364/OL.25.001502. PMID 18066259. tures. The first superprism also modified group velocity • rather than phase velocity in order to achieve the “su- Matsumoto T, Fujita S, Baba T (2005). “Wave- perprism phenomena”. This effect was interpreted as length demultiplexer consisting of Photonic crys- anisotropic dispersion in contrast to an isotropic disper- tal superprism and superlens”. Optics Express 13 sion. Furthermore, the two beams of light appear to show (26): 10768–76. Bibcode:2005OExpr..1310768M. negative bending within the crystal.[1] doi:10.1364/OPEX.13.010768. PMID 19503294. • Witzens J, Baehr-Jones T, Scherer A (2005). “Hybrid superprism with low insertion losses and 7.1 See also suppressed cross-talk” (PDF). Physical Review E 71: 026604. Bibcode:2005PhRvE..71a6604W. doi:10.1103/PhysRevE.71.016604. • Superlens • Momeni B, Huang J, Soltani M, Askari M, • Prism (optics) Mohammadi S, Rakhshandehroo M, Adibi A (2006). “Compact wavelength demultiplex- • Metamaterial ing using focusing negative index photonic • Perfect mirror crystal superprisms”. Optics Express 14 (6): 2413–22. Bibcode:2006OExpr..14.2413M. doi:10.1364/OE.14.002413. PMID 19503580. 7.2 References • Jugessur A, Wu L, Bakhtazad A, Kirk A, Krauss T, De La Rue R (2006). “Compact and integrated 2-D [1] Kosaka, Hideo; Kawashima, Takayuki; Tomita, photonic crystal super-prism filter-device for wave- Akihisa; Notomi, Masaya; Tamamura, Toshi- length demultiplexing applications”. Optics Express aki; Sato, Takashi; Kawakami, Shojiro (1998). 14 (4): 1632–42. Bibcode:2006OExpr..14.1632J. “Superprism phenomena in photonic crystals” doi:10.1364/OE.14.001632. PMID 19503491. (FREE PDF DOWNLOAD). Physical Review B 58 (16): R10096. Bibcode:1998PhRvB..5810096K. doi:10.1103/PhysRevB.58.R10096.

7.3 Further reading

• Prasad T, Colvin V, Mittleman D (2003). “Superprism phenomenon in three-dimensional macroporous polymer photonic crys- tals” (PDF). Physical Review B 67 (16): 165103. Bibcode:2003PhRvB..67p5103P. doi:10.1103/PhysRevB.67.165103.

25 26 CHAPTER 7. SUPERPRISM

7.4 Text and image sources, contributors, and licenses

7.4.1 Text

• Spectrometer Source: https://en.wikipedia.org/wiki/Spectrometer?oldid=676465986 Contributors: Vsmith, Kkmurray, HPaul, Ronningt, Download, Tom.Reding, ClueBot NG, BG19bot, Crystallizedcarbon, KasparBot and Anonymous: 3 • Prism Source: https://en.wikipedia.org/wiki/Prism?oldid=683039989 Contributors: DrBob, Patrick, Michael Hardy, Glenn, Tantalate, Saltine, Robbot, Hankwang, Chris 73, Altenmann, DHN, Hadal, Xanzzibar, Reytan, Mintleaf~enwiki, Fudoreaper, BenFrantzDale, Ævar Arnfjörð Bjarmason, AJim, Andycjp, Chris Howard, Bumphoney, Magic5ball, Vsmith, Pavel Vozenilek, El C, Huntster, Semper discens, Smalljim, Flammifer, Einar Myre, Mareino, Jumbuck, Snowolf, Lokedhs, Sakus, Alai, HenryLi, Kazvorpal, Kmg90, Xiong, Nanite, Saper- aud~enwiki, TeemuN, Johnrpenner, FlaBot, RexNL, Srleffler, Spencerk, Johnpenner, Bgwhite, YurikBot, RobotE, RussBot, SpuriousQ, Eleassar, Wimt, ErkDemon, DeadEyeArrow, BorgQueen, JoanneB, Alexandrov, GrinBot~enwiki, Cmglee, SmackBot, Gilliam, Saros136, DHN-bot~enwiki, Can't sleep, clown will eat me, MastaTKK367, Lizzielizzielizzie, SundarBot, CanDo, Baby-g, Jidanni, Robofish, Iron- Gargoyle, Grumpyyoungman01, Dicklyon, Citicat, Tawkerbot2, NickSpiker, Karenjc, Meno25, Gogo Dodo, Quibik, Vanished User jdks- fajlasd, Justinp93, PKT, Michael Fourman, Thijs!bot, Headbomb, Rlupsa, Escarbot, AntiVandalBot, Widefox, BailesB, Tomorrow Never Knows, Magioladitis, RogierBrussee, VoABot II, MartinBot, CommonsDelinker, J.delanoy, Hans Dunkelberg, Acalamari, Rod57, Shawn in Montreal, Afluegel, Joshua Issac, DorganBot, D-Kuru, VolkovBot, NathanHagen, TXiKiBoT, NPrice, Qxz, LeaveSleaves, Cremepuff222, Trueemo, Spinningspark, AlleborgoBot, Symane, SieBot, Trent17 99, Gerakibot, Dawn Bard, Caltas, Flyer22, Aruton, Oxymoron83, An- tonio Lopez, WingkeeLEE, BenoniBot~enwiki, ClueBot, Frdayeen, Adrian dakota, Manishearth, Paul Pot, Computer97, Thingg, Versus22, Adrian Teh, Darkicebot, XLinkBot, RP459, Addbot, Guoguo12, Jncraton, CanadianLinuxUser, Chzz, Tide rolls, Arnoques, Luckas-bot, Amirobot, Rrokkedd, AnomieBOT, Ciphers, Jim1138, Materialscientist, Citation bot, ArthurBot, Xqbot, Corrigendas, Frosted14, Ribot- BOT, Doulos Christos, Captain-n00dle, Hexicola, D'ohBot, Steve Quinn, Craig Pemberton, Valerian456, Lskil09, Pinethicket, Monkey- fox, Dinamik-bot, UNIT A4B1, Weedwhacker128, TheMesquito, Marie Poise, TjBot, Ripchip Bot, Nyxaus, Petar607, EmausBot, Orphan Wiki, ZéroBot, Josve05a, AManWithNoPlan, ClueBot NG, CocuBot, Widr, Aniketmh035569, Helpful Pixie Bot, Sandro-xxx, Bibcode Bot, Jeraphine Gryphon, Wikgeek11, Tom Pippens, NotWith, Achowat, Lugia2453, SFK2, Telfordbuck, 069952497a, NottNott, Quenhi- tran, Smellypoos, Kali David Heffernan, Argailyasa, Xturtle MasterX, Amortias, Speakfromthesoul, ToonLucas22, Alex macneil, Clicksm, KasparBot, Bobtobs, G.Edenhofer and Anonymous: 226 • Minimum deviation Source: https://en.wikipedia.org/wiki/Minimum_deviation?oldid=670193920 Contributors: David Gerard, Icairns, Kwamikagami, SmackBot, Pieter Kuiper, Wayne Miller, Biscuittin, WingkeeLEE, KathrynLybarger, ClueBot, Yobot, Capricorn42, PhysicsR, GoingBatty, Gowtham vmj, Scientific29, Cjb9212, Mogism, SiBr4, Supdiop and Anonymous: 18 • Angle of incidence Source: https://en.wikipedia.org/wiki/Angle_of_incidence?oldid=671348001 Contributors: Fubar Obfusco, SimonP, Maury Markowitz, Michael Hardy, Sergiusz Patela, Theresa knott, GRAHAMUK, Syclop, UtherSRG, BenFrantzDale, Frencheigh, Vess- bot, Tomruen, Trevor MacInnis, Rich Farmbrough, CanisRufus, Bobo192, Meggar, Mac Davis, IMeowbot, Shoefly, Eaolson, Rjwilmsi, Vegaswikian, Maustrauser, Srleffler, Kri, Chobot, Splintercellguy, Ssbohio, Moralis, Bluebot, Viewfinder, Eynar, UVnet, Pflatau, 16@r, Dicklyon, JMK, Domitori, Tawkerbot2, Cydebot, Matt.S., KrakatoaKatie, AntiVandalBot, Akradecki, RebelRobot, VoABot II, Cat- slash, Appraiser, Andreas 06, Nobuts, Bdodo1992, Kyle the bot, Bosoxs 2000, Madhero88, Robo.mind, Blood sliver, Struway, Manway, Spooky1966, Dolphin51, Muhends, ClueBot, Ideal gas equation, Ariadacapo, DumZiBoT, WikHead, RyanCross, Addbot, Fgnievinski, Fieldday-sunday, Coffeeassured, Mpfiz, Yobot, Ptbotgourou, AnomieBOT, Agentex, Erik9bot, Gummer85, Pinethicket, FrozenPencil, DexDor, Mikko raikkonen, Torturella, Wikipelli, Hhhippo, Joshua Doubek, MonoAV, ChuispastonBot, ClueBot NG, Jay8g, Mrt3366, Josell2, Filedelinkerbot, Neilstraus and Anonymous: 59 • Refractive index Source: https://en.wikipedia.org/wiki/Refractive_index?oldid=684659646 Contributors: Bryan Derksen, Tarquin, XJaM, Fredbauder, DrBob, Bdesham, Michael Hardy, W~enwiki, Fwappler, Looxix~enwiki, Ellywa, Stevenj, Tantalate, Andrevan, Max- imus Rex, Donarreiskoffer, Gentgeen, Robbot, Hankwang, Eman, RedWolf, Yelyos, Chris Roy, Robinh, Diberri, Syntax~enwiki, Centrx, Giftlite, Smjg, Harp, BenFrantzDale, Xerxes314, TomViza, Hugh2414, Nayuki, Jurema Oliveira, Selva, Aulis Eskola, Grm wnr, Danh, L- H, Geof, DanielCD, Rich Farmbrough, Vsmith, R6144, Graceej, Rgdboer, Causa sui, Kjkolb, RPaschotta, Neonumbers, Keenan Pepper, Benjah-bmm27, MattWade, Velella, Dirac1933, Oleg Alexandrov, Linas, Jimbryho, JonBirge, Wurzel~enwiki, Isnow, Bobmilkman, Seven- tyThree, GraemeLeggett, Askewmind, Graham87, Rjwilmsi, Ceinturion, MZMcBride, S Schaffter, FlaBot, Weihao.chiu~enwiki, Arnero, Latka, DrVeghead, Fresheneesz, Goudzovski, Srleffler, Chobot, YurikBot, RobotE, Rowan Moore, Pigman, Sasuke Sarutobi, Kirill Lok- shin, Chrisada~enwiki, TDogg310, Dbfirs, Bota47, Rallette, Elkman, Petri Krohn, GraemeL, Pentasyllabic, Sbyrnes321, Finell, SmackBot, RDBury, The Photon, Gilliam, Jlsilva, Marc Kupper, Chris the speller, Bluebot, Oli Filth, Leifisme, Complexica, Metacomet, Jfsamper, DHN-bot~enwiki, A. B., Can't sleep, clown will eat me, Nick Levine, Mpolianski~enwiki, Smokefoot, Jbergquist, Mwtoews, DMacks, Rhkramer, JMO, Stefano85, Lambiam, Akhlesh, Nick Green, Mksword, Pflatau, Jonasbinding, Mr Stephen, Rogerbrent, Erwin, MTS- bot~enwiki, Vincecate, DabMachine, Pgadfor, Mrainer, Andreas Rejbrand, Jaksmata, Tawkerbot2, Hammer Raccoon, Kingoomieiii, Do- ,הסרפד ,manix, Chrumps, NickSpiker, Aubrey Jaffer, Icek~enwiki, Cydebot, Difluoroethene, Skittleys, SteveMcCluskey, Msebast~enwiki Barticus88, Frozenport, Headbomb, Pjvpjv, John254, Timbercon, Ingolfson, CosineKitty, Swpb, Georgeasdf, UnaLaguna, Daarznieks, JJ Harrison, DerHexer, Hbent, MartinBot, CommonsDelinker, Extransit, Nemo bis, Afluegel, Mikael Häggström, Chiswick Chap, BigHair- Ref, Squids and Chips, VolkovBot, DeftTechie, TXiKiBoT, Martin451, Falcon8765, Zebas, Jovial Air, Gerakibot, Jason Patton, Keilana, Pigletion, Sunrise, Spitfire19, Wsmith202~enwiki, Klsyking, ClueBot, Pointillist, Awickert, Gnome de plume, Eeekster, Rwestafer, Brews ohare, Arjayay, SchreiberBike, ChrisHodgesUK, Omer88f, Crowsnest, RexxS, Forbes72, Deszoeke, Boyfarrell, Srhat, Addbot, DOI bot, Fgnievinski, TutterMouse, Fluffernutter, Asymptotic wiki, MrOllie, Download, CarsracBot, TStein, Bob K31416, Tide rolls, Finley08, Gail, Zorrobot, Quantumobserver, Skippy le Grand Gourou, Luckas-bot, Yobot, Amirobot, Litherum, Gelbukh, Feldkurat Katz, AnomieBOT, Rubinbot, AdjustShift, Materialscientist, Citation bot, ArthurBot, Xqbot, Nasnema, Anon423, Raffamaiden, Turk oğlan, NOrbeck, A. di M., Acky69, Paisiello2, K217, DKToptics, Mfwitten, Steve Quinn, Dome1ioun1, DivineAlpha, Citation bot 1, Maggyero, Pinethicket, Matt.urq, Ionelenadaniela, Gryllida, Orenburg1, Double sharp, 0x30114, LogAntiLog, RjwilmsiBot, TheArguer, Mod mmg, Ankid, Yuhuach, VoteITP, Racerx11, Koilon, Δ, Brandmeister, Donner60, Carmichael, RockMagnetist, Hiukkas, Mjbmrbot, Thuytnguyen48, ClueBot NG, Ulflund, Pradeep717, Gilderien, Wgolf, Touchlee, Helpful Pixie Bot, Bibcode Bot, BG19bot, Yosemite29brandon, Nsda, Jeffluo1011, Skkies, Vswitchs, Wannabemodel, 786b6364, Graphium, Josell2, Reatlas, ChrisCharma, PC-XT, Antuanne, Visura1, Izhaq, Monkbot, Martinmagnuson, Nandktech, Votingstar, TaeYunPark, Colin2702, Bunnycarrot9898, David G Pedia, Bobfelix38, Kekking434, KiarashKevin, Tranttipsy8888, Intrinsico, WhyWillSheNotDoTheNastyWithMe and Anonymous: 290 • Prism spectrometer Source: https://en.wikipedia.org/wiki/Prism_spectrometer?oldid=684457415 Contributors: Srleffler, Stefan2, Philg88, Revent, Yobot, Elee, Josve05a, BattyBot and G.Edenhofer 7.4. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 27

• Superprism Source: https://en.wikipedia.org/wiki/Superprism?oldid=580822505 Contributors: Srleffler, Light current, Banus, Smack- Bot, M.luke.myers, Thumperward, Fabo47, MarshBot, Gioto, Katharineamy, Yobot, AnomieBOT, Citation bot, Bmomeni, Steve Quinn, Citation bot 1, Bibcode Bot and Anonymous: 3

7.4.2 Images • File:Aircraft_Angle_of_Incidence_(improved)-$-$1080x660-$-$25Mar2009.jpg Source: https://upload.wikimedia.org/wikipedia/ en/0/0e/Aircraft_Angle_of_Incidence_%28improved%29-$-$1080x660-$-$25Mar2009.jpg License: PD Contributors: Own work Original artist: Gummer85 (talk)(Uploads) • File:Angle_of_incidence.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/30/Angle_of_incidence.svg License: Public domain Contributors: Own work Original artist: Andreas 06 • File:Brillanten.jpg Source: https://upload.wikimedia.org/wikipedia/commons/6/6f/Brillanten.jpg License: CC-BY-SA-3.0 Contributors: Self-photographed Original artist: Mario Sarto • File:Calcite.jpg Source: https://upload.wikimedia.org/wikipedia/commons/7/7a/Calcite.jpg License: Public domain Contributors: ? Orig- inal artist: ? • File:Commons-logo.svg Source: https://upload.wikimedia.org/wikipedia/en/4/4a/Commons-logo.svg License: ? Contributors: ? Original artist: ? • File:Comparison_refraction_diffraction_spectra.svg Source: https://upload.wikimedia.org/wikipedia/commons/1/10/Comparison_ refraction_diffraction_spectra.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Cmglee • File:Deflection_of_light_ray_passing_through_prism.png Source: https://upload.wikimedia.org/wikipedia/commons/9/98/ Deflection_of_light_ray_passing_through_prism.png License: CC BY-SA 3.0 Contributors: created in powerpoint Original artist: PhysicsR • File:Density-nd.GIF Source: https://upload.wikimedia.org/wikipedia/en/3/3b/Density-nd.GIF License: PD Contributors: ? Original artist: ? • File:Deviation_angle_of_a_beam_of_light_entering_a_medium_with_refractive_index.png Source: https://upload.wikimedia.org/ wikipedia/commons/4/4c/Deviation_angle_of_a_beam_of_light_entering_a_medium_with_refractive_index.png License: CC0 Contrib- utors: PowerPoint Original artist: PhysicsR • File:Dispersion-curve.png Source: https://upload.wikimedia.org/wikipedia/commons/2/20/Dispersion-curve.png License: CC-BY-SA- 3.0 Contributors: Transferred from en.wikipedia to Commons. Original artist: DrBob at English Wikipedia • File:Experiment_setup.svg Source: https://upload.wikimedia.org/wikipedia/commons/9/90/Experiment_setup.svg License: CC BY-SA 4.0 Contributors: Own work Original artist: Gordian Edenhofer • File:Experiment_setup_(high_angle_with_light).svg Source: https://upload.wikimedia.org/wikipedia/en/d/da/Experiment_setup_ %28high_angle_with_light%29.svg License: CC-BY-SA-3.0 Contributors: own work Original artist: Gordian Edenhofer • File:Experiment_setup_(low_angle_with_light).svg Source: https://upload.wikimedia.org/wikipedia/en/0/03/Experiment_setup_ %28low_angle_with_light%29.svg License: CC-BY-SA-3.0 Contributors: own work Original artist: Gordian Edenhofer • File:Focus01.png Source: https://upload.wikimedia.org/wikipedia/commons/4/4b/Focus01.png License: CC BY-SA 4.0 Contributors: Own work Original artist: HPaul • File:FuerzaCentripetaLorentzP.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a9/FuerzaCentripetaLorentzP.svg Li- cense: CC BY-SA 3.0 Contributors: Own work Original artist: Jfmelero • File:Gradndfilter.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/c2/Gradndfilter.jpg License: CC BY-SA 2.5 Contrib- utors: Transferred from en.wikipedia to Commons. Original artist: Ziggur at English Wikipedia • File:Grin-lens.png Source: https://upload.wikimedia.org/wikipedia/commons/2/2c/Grin-lens.png License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Lens_triplet.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/74/Lens_triplet.svg License: CC-BY-SA-3.0 Contrib- utors: Image:Lens triplet.png Original artist: Panther, Antilived • File:Light_dispersion_conceptual_waves.gif Source: https://upload.wikimedia.org/wikipedia/commons/f/f5/Light_dispersion_ conceptual_waves.gif License: Public domain Contributors: ? Original artist: ? • File:Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr°0125.jpg Source: https://upload.wikimedia. org/wikipedia/commons/1/1f/Light_dispersion_of_a_mercury-vapor_lamp_with_a_flint_glass_prism_IPNr%C2%B00125.jpg License: CC BY-SA 3.0 at Contributors: Own work Original artist: D-Kuru • File:Lupa.na.encyklopedii.jpg Source: https://upload.wikimedia.org/wikipedia/commons/f/f4/Lupa.na.encyklopedii.jpg License: Pub- lic domain Contributors: Own work Original artist: Julo • File:Minimum_deflection_of_light_ray_passing_through_prism.png Source: https://upload.wikimedia.org/wikipedia/commons/e/ e0/Minimum_deflection_of_light_ray_passing_through_prism.png License: CC BY-SA 3.0 Contributors: created in powerpoint Original artist: PhysicsR 28 CHAPTER 7. SUPERPRISM

• File:Plastic_Protractor_Polarized_05375.jpg Source: https://upload.wikimedia.org/wikipedia/commons/e/e4/Plastic_Protractor_ Polarized_05375.jpg License: CC-BY-SA-3.0 Contributors: Own Photograph Original artist: Nevit Dilmen • File:Prism-side-fs_PNr°0117.jpg Source: https://upload.wikimedia.org/wikipedia/commons/c/cd/Prism-side-fs_PNr%C2%B00117. jpg License: CC BY-SA 3.0 at Contributors: Own work Original artist: D-Kuru • File:Prism_rainbow_schema.png Source: https://upload.wikimedia.org/wikipedia/commons/0/06/Prism_rainbow_schema.png License: CC-BY-SA-3.0 Contributors: ? Original artist: ? • File:Prism_ray_trace.svg Source: https://upload.wikimedia.org/wikipedia/commons/7/7d/Prism_ray_trace.svg License: PD Contribu- tors: ? Original artist: ? • File:Pulfrich_refraktometer_en.png Source: https://upload.wikimedia.org/wikipedia/commons/e/ed/Pulfrich_refraktometer_en.png License: CC BY-SA 2.5 Contributors: No machine-readable source provided. Own work assumed (based on copyright claims). Origi- nal artist: No machine-readable author provided. Kodak17~commonswiki assumed (based on copyright claims). • File:Question_book-new.svg Source: https://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg License: Cc-by-sa-3.0 Contributors: Created from scratch in Adobe Illustrator. Based on Image:Question book.png created by User:Equazcion Original artist: Tkgd2007 • File:RefractionReflextion.svg Source: https://upload.wikimedia.org/wikipedia/commons/5/5d/RefractionReflextion.svg License: CC BY-SA 3.0 Contributors: Own work Original artist: Josell7 • File:Refraction_at_interface.svg Source: https://upload.wikimedia.org/wikipedia/commons/3/3f/Refraction_at_interface.svg License: CC0 Contributors: Own work Original artist: Ulflund • File:Refraction_photo.png Source: https://upload.wikimedia.org/wikipedia/commons/8/85/Refraction_photo.png License: Public do- main Contributors: http://www.docstoc.com/docs/130534946/Chapter-7-Refractive-index Original artist: ajizai • File:Refractometer.jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/9e/Refractometer.jpg License: CC-BY-SA-3.0 Contributors: Own work Original artist: Fernando G. (FGM) • File:S_cerevisiae_under_DIC_microscopy.jpg Source: https://upload.wikimedia.org/wikipedia/commons/d/d9/S_cerevisiae_under_ DIC_microscopy.jpg License: Public domain Contributors: Own work Original artist: Masur • File:Science.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/54/Science.jpg License: Public domain Contributors: ? Original artist: ? • File:Snells_law.svg Source: https://upload.wikimedia.org/wikipedia/commons/d/d1/Snells_law.svg License: Public domain Contributors: Transferred from en.wikipedia to Commons. Original artist: Cristan at English Wikipedia • File:Soap_bubble_sky.jpg Source: https://upload.wikimedia.org/wikipedia/commons/1/18/Soap_bubble_sky.jpg License: CC-BY-SA- 3.0 Contributors: Own work Original artist: Brocken Inaglory • File:Split-ring_resonator_array_10K_sq_nm.jpg Source: https://upload.wikimedia.org/wikipedia/commons/8/82/Split-ring_ resonator_array_10K_sq_nm.jpg License: Public domain Contributors: NASA Glenn Research Original artist: Jeff[email protected] (Glenn research contact) • File:Text_document_with_red_question_mark.svg Source: https://upload.wikimedia.org/wikipedia/commons/a/a4/Text_document_ with_red_question_mark.svg License: Public domain Contributors: Created by bdesham with Inkscape; based upon Text-x-generic.svg from the Tango project. Original artist: Benjamin D. Esham (bdesham) • File:Thomas_Young_(scientist).jpg Source: https://upload.wikimedia.org/wikipedia/commons/9/9f/Thomas_Young_%28scientist% 29.jpg License: Public domain Contributors: National Portrait Gallery: NPG 1899D7714, also on gutenberg.org Original artist: After Thomas Lawrence • File:Total_internal_reflection_of_Chelonia_mydas.jpg Source: https://upload.wikimedia.org/wikipedia/commons/5/5c/Total_ internal_reflection_of_Chelonia_mydas.jpg License: GFDL Contributors: Own work Original artist: Brocken Inaglory • File:WhereRainbowRises.jpg Source: https://upload.wikimedia.org/wikipedia/commons/2/27/WhereRainbowRises.jpg License: CC BY-SA 2.5 Contributors: self-made; at Jasper National Park, Alberta, Canada (along Yellowhead Highway 16 between intersection to Malign Valley Road and intersection to Snaring River Campground, overlooking Colin Range in the south). Original artist: Wing-Chi Poon

7.4.3 Content license

• Creative Commons Attribution-Share Alike 3.0