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Chapter 6 Prism Spectrometer 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
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