1 Diffraction of Visible Light Emily Coats Lab 8 Visible Light Has an In
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Diffraction Grating Experiments Warning: Never Point Any Laser Into Your Own Or Other People’S Eyes
Diffraction grating experiments Warning: Never point any laser into your own or other people’s eyes. Materials and tools Diffraction glasses (diffraction grating 1000 lines/mm) Flashlight Laser pointers (red, green, blue) Other light sources (light bulbs, arc lamps, etc.) Rulers White paper for screen Binder clips Graphing paper or computer graphing tools Scientific calculator In these experiments you will use diffraction glasses to perform measurements of light diffraction. Diffraction is a phenomenon that is due to the wave-like nature of light. Predict 1. What do you think will happen when you shine white light through a prism and why? Draw a picture to show your predictions. When white light goes through a diffraction grating (diffraction glasses), different colors are bent a different angles, similar to how they are bent be a prism. 2. (a) What do you think will happen when you shine red laser light through the diffraction glasses? (b) What do you think will happen when you shine blue laser light through the diffraction glasses? (c) Draw a picture to show your predictions. Experiment setup 1. For a projection screen, use a white wall, or use binder clips to make a white screen out of paper. 2. Use binder clips to make your diffraction glasses stand up. 3. Secure a light source with tape as needed. 4. Insert a piece of colored plastic between the source and the diffraction grating as needed. Observation 1. Shine white light through the diffraction glasses and observe the pattern projected on a white screen. Adjust the angle between the beam of light and the glasses to get a symmetric pattern as in the figure above. -
Phase Retrieval Without Prior Knowledge Via Single-Shot Fraunhofer Diffraction Pattern of Complex Object
Phase retrieval without prior knowledge via single-shot Fraunhofer diffraction pattern of complex object An-Dong Xiong1 , Xiao-Peng Jin1 , Wen-Kai Yu1 and Qing Zhao1* Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the lost phase part is indispensable for reverse transformation. Phase retrieval is usually conducted in two means: priori knowledge or multiple different measurements. However, priori knowledge works for certain type of object while multiple measurements are difficult for short wavelength. Here, by introducing non-orthogonal measurement via high density sampling scheme, we demonstrate that one single-shot Fraunhofer diffraction pattern of complex object is sufficient for phase retrieval. Both simulation and experimental results have demonstrated the feasibility of our scheme. Reconstruction of complex object reveals depth information or refraction index; and single-shot measurement can be achieved under most scenario. Their combination will broaden the application field of coherent diffraction imaging. Fraunhofer diffraction, also known as far-field diffraction, problem12-14. These matrix complement methods require 4N- does not necessarily need any extra optical devices except a 4 (N stands for the dimension) generic measurements such as beam source. The diffraction field is the Fourier transform of Gaussian random measurements for complex field15. the original light field. However, for visible light or X-ray Ptychography is another reliable method to achieve image diffraction, the phase part is hardly directly measurable1. with good resolution if the sample can endure scanning16-19. Therefore, phase retrieval from intensity measurement To achieve higher spatial resolution around the size of atom, becomes necessary for reconstructing the original field. -
Lab 4: DIFFRACTION GRATINGS and PRISMS (3 Lab Periods)
revised version Lab 4: DIFFRACTION GRATINGS AND PRISMS (3 Lab Periods) Objectives Calibrate a diffraction grating using a spectral line of known wavelength. With the calibrated grating, determine the wavelengths of several other spectral lines. De- termine the chromatic resolving power of the grating. Determine the dispersion curve (refractive index as a function of wavelength) of a glass prism. References Hecht, sections 3.5, 5.5, 10.2.8; tables 3.3 and 6.2 (A) Basic Equations We will discuss diffraction gratings in greater detail later in the course. In this laboratory, you will need to use only two basic grating equations, and you will not need the details of the later discussion. The first equation should be familiar to you from an introductory Physics course and describes the angular positions of the principal maxima of order m for light of wavelength λ. (4.1) where a is the separation between adjacent grooves in the grating. The other, which may not be as familiar, is the equation for the chromatic resolving power Rm in the diffraction order m when N grooves in the grating are illuminated. (4.2) where (Δλ)min is the smallest wavelength difference for which two spectral lines, one of wave- length λ and the other of wavelength λ + Δλ, will just be resolved. The absolute value insures that R will be a positive quantity for either sign of Δλ. If Δλ is small, as it will be in this experiment, it does not matter whether you use λ, λ + Δλ, or the average value in the numerator. -
Fresnel Diffraction.Nb Optics 505 - James C
Fresnel Diffraction.nb Optics 505 - James C. Wyant 1 13 Fresnel Diffraction In this section we will look at the Fresnel diffraction for both circular apertures and rectangular apertures. To help our physical understanding we will begin our discussion by describing Fresnel zones. 13.1 Fresnel Zones In the study of Fresnel diffraction it is convenient to divide the aperture into regions called Fresnel zones. Figure 1 shows a point source, S, illuminating an aperture a distance z1away. The observation point, P, is a distance to the right of the aperture. Let the line SP be normal to the plane containing the aperture. Then we can write S r1 Q ρ z1 r2 z2 P Fig. 1. Spherical wave illuminating aperture. !!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!! 2 2 2 2 SQP = r1 + r2 = z1 +r + z2 +r 1 2 1 1 = z1 + z2 + þþþþ r J þþþþþþþ + þþþþþþþN + 2 z1 z2 The aperture can be divided into regions bounded by concentric circles r = constant defined such that r1 + r2 differ by l 2 in going from one boundary to the next. These regions are called Fresnel zones or half-period zones. If z1and z2 are sufficiently large compared to the size of the aperture the higher order terms of the expan- sion can be neglected to yield the following result. l 1 2 1 1 n þþþþ = þþþþ rn J þþþþþþþ + þþþþþþþN 2 2 z1 z2 Fresnel Diffraction.nb Optics 505 - James C. Wyant 2 Solving for rn, the radius of the nth Fresnel zone, yields !!!!!!!!!!! !!!!!!!! !!!!!!!!!!! rn = n l Lorr1 = l L, r2 = 2 l L, , where (1) 1 L = þþþþþþþþþþþþþþþþþþþþ þþþþþ1 + þþþþþ1 z1 z2 Figure 2 shows a drawing of Fresnel zones where every other zone is made dark. -
WHITE LIGHT and COLORED LIGHT Grades K–5
WHITE LIGHT AND COLORED LIGHT grades K–5 Objective This activity offers two simple ways to demonstrate that white light is made of different colors of light mixed together. The first uses special glasses to reveal the colors that make up white light. The second involves spinning a colorful top to blend different colors into white. Together, these activities can be thought of as taking white light apart and putting it back together again. Introduction The Sun, the stars, and a light bulb are all sources of “white” light. But what is white light? What we see as white light is actually a combination of all visible colors of light mixed together. Astronomers spread starlight into a rainbow or spectrum to study the specific colors of light it contains. The colors hidden in white starlight can reveal what the star is made of and how hot it is. The tool astronomers use to spread light into a spectrum is called a spectroscope. But many things, such as glass prisms and water droplets, can also separate white light into a rainbow of colors. After it rains, there are often lots of water droplets in the air. White sunlight passing through these droplets is spread apart into its component colors, creating a rainbow. In this activity, you will view the rainbow of colors contained in white light by using a pair of “Rainbow Glasses” that separate white light into a spectrum. ! SAFETY NOTE These glasses do NOT protect your eyes from the Sun. NEVER LOOK AT THE SUN! Background Reading for Educators Light: Its Secrets Revealed, available at http://www.amnh.org/education/resources/rfl/pdf/du_x01_light.pdf Developed with the generous support of The Charles Hayden Foundation WHITE LIGHT AND COLORED LIGHT Materials Rainbow Glasses Possible white light sources: (paper glasses containing a Incandescent light bulb diffraction grating). -
Diffraction Grating and the Spectrum of Light
DIFFRACTION GRATING OBJECTIVE: To use the diffraction grating in the formation of spectra and in the measurement of wavelengths. THEORY: The operation of the grating is depicted in Fig. 1 on page 3. Lens 1 produces a parallel beam of light from the single slit source A to the diffraction grating. The grating itself consists of a large number of very narrow transparent slits equally spaced with a distance D between adjacent slits. The light rays numbered 1, 2, 3, etc. represent those rays which are diffracted at an angle by the grating. Lens 2 is used to focus these rays to a line image at B. Notice that ray 2 travels a distance x = D sin more than 1, ray 3 travels x more than 2, etc. When the extra distance traveled is one wavelength, two wavelengths, or N wavelengths, constructive interference occurs. Thus, bright images of a monochromatic (single color) source of wavelength will occur at position B at a diffraction angle if Sin(N) = N / D where N = 0, 1, 2, 3, ... (1) The images generally are brightest for N=0 (0 = 0), and become corresponding less bright for higher N. Since, for a given value of N, the angle at which constructive interference occurs depends on , a polychromatic light source will produce a SERIES of single color bright images. There will be an image for each wavelength radiated by the source. Each image will have a color corresponding to its wavelength, and each image will be formed at a different angle. In this manner a spectrum of the light source is formed by the grating. -
Fraunhofer Diffraction Effects on Total Power for a Planckian Source
Volume 106, Number 5, September–October 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 775–779 (2001)] Fraunhofer Diffraction Effects on Total Power for a Planckian Source Volume 106 Number 5 September–October 2001 Eric L. Shirley An algorithm for computing diffraction ef- Key words: diffraction; Fraunhofer; fects on total power in the case of Fraun- Planckian; power; radiometry. National Institute of Standards and hofer diffraction by a circular lens or aper- Technology, ture is derived. The result for Fraunhofer diffraction of monochromatic radiation is Gaithersburg, MD 20899-8441 Accepted: August 28, 2001 well known, and this work reports the re- sult for radiation from a Planckian source. [email protected] The result obtained is valid at all temper- atures. Available online: http://www.nist.gov/jres 1. Introduction Fraunhofer diffraction by a circular lens or aperture is tion, because the detector pupil is overfilled. However, a ubiquitous phenomenon in optics in general and ra- diffraction leads to losses in the total power reaching the diometry in particular. Figure 1 illustrates two practical detector. situations in which Fraunhofer diffraction occurs. In the All of the above diffraction losses have been a subject first example, diffraction limits the ability of a lens or of considerable interest, and they have been considered other focusing optic to focus light. According to geo- by Blevin [2], Boivin [3], Steel, De, and Bell [4], and metrical optics, it is possible to focus rays incident on a Shirley [5]. The formula for the relative diffraction loss lens to converge at a focal point. -
25-2 the Diffraction Grating
Answer to Essential Question 25.1 (a) The only points for which changing the wavelength has no impact on the interference of the waves are points for which the path-length difference is zero. Thus, the point in question must lie on the perpendicular bisector of the line joining the sources. (b) If we re-arrange Equation 25.3 to solve for the sine of the angle, we get . Thus, decreasing the wavelength decreases sin θ, so the pattern gets tighter. Decreasing d, the distance between the sources, has the opposite effect, with the pattern spreading out. We can understand the wavelength effect conceptually in that, when the wavelength decreases, we don’t have to go as far from the perpendicular bisector to locate points that are half a wavelength (or a full wavelength) farther from one source than the other. Figure 25.3 shows the effect of decreasing the wavelength, or of decreasing the distance between the sources. Figure 25.3: The top diagram shows the interference pattern produced by two sources. The middle diagram shows the effect of decreasing the wavelength of the waves produced by the sources, while the bottom diagram shows the effect of decreasing the distance between the sources. 25-2 The Diffraction Grating Now that we understand what happens when we have two sources emitting waves that interfere, let’s see if we can understand what happens when we add additional sources. The distance d between neighboring sources is the same as the distance between the original two sources, and the sources are arranged in a line. -
Fraunhofer Diffraction with a Laser Source
Second Year Laboratory Fraunhofer Diffraction with a Laser Source L3 ______________________________________________________________ Health and Safety Instructions. There is no significant risk to this experiment when performed under controlled laboratory conditions. However: • This experiment involves the use of a class 2 diode laser. This has a low power, visible, red beam. Eye damage can occur if the laser beam is shone directly into the eye. Thus, the following safety precautions MUST be taken:- • Never look directly into the beam. The laser key, which is used to switch the laser on and off, preventing any accidents, must be obtained from and returned to the lab technician before and after each lab session. • Do not remove the laser from its mounting on the optical bench and do not attempt to use the laser in any other circumstances, except for the recording of the diffraction patterna. • Be aware that the laser beam may be reflected off items such as jewellery etc ______________________________________________________________ 26-09-08 Department of Physics and Astronomy, University of Sheffield Second Year Laboratory 1. Aims The aim of this experiment is to study the phenomenon of diffraction using monochromatic light from a laser source. The diffraction patterns from single and multiple slits will be measured and compared to the patterns predicted by Fourier methods. Finally, Babinet’s principle will be applied to determine the width of a human hair from the diffraction pattern it produces. 2. Apparatus • Diode Laser – see Laser Safety Guidelines before use, • Photodiode, • Optics Bench, • Traverse, • Box of apertures, • PicoScope Analogue to Digital Converter, • Voltmeter, • Personal Computer. 3. Background (a) General The phenomenon of diffraction occurs when waves pass through an aperture whose width is comparable to their wavelength. -
Huygens Principle; Young Interferometer; Fresnel Diffraction
Today • Interference – inadequacy of a single intensity measurement to determine the optical field – Michelson interferometer • measuring – distance – index of refraction – Mach-Zehnder interferometer • measuring – wavefront MIT 2.71/2.710 03/30/09 wk8-a- 1 A reminder: phase delay in wave propagation z t t z = 2.875λ phasor due In general, to propagation (path delay) real representation phasor representation MIT 2.71/2.710 03/30/09 wk8-a- 2 Phase delay from a plane wave propagating at angle θ towards a vertical screen path delay increases linearly with x x λ vertical screen (plane of observation) θ z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 3 Phase delay from a spherical wave propagating from distance z0 towards a vertical screen x z=z0 path delay increases quadratically with x λ vertical screen (plane of observation) z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 4 The significance of phase delays • The intensity of plane and spherical waves, observed on a screen, is very similar so they cannot be reliably discriminated – note that the 1/(x2+y2+z2) intensity variation in the case of the spherical wave is too weak in the paraxial case z>>|x|, |y| so in practice it cannot be measured reliably • In many other cases, the phase of the field carries important information, for example – the “history” of where the field has been through • distance traveled • materials in the path • generally, the “optical path length” is inscribed -
Monte Carlo Ray-Trace Diffraction Based on the Huygens-Fresnel Principle
Monte Carlo Ray-Trace Diffraction Based On the Huygens-Fresnel Principle J. R. MAHAN,1 N. Q. VINH,2,* V. X. HO,2 N. B. MUNIR1 1Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA 2Department of Physics and Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, VA 24061, USA *Corresponding author: [email protected] The goal of this effort is to establish the conditions and limits under which the Huygens-Fresnel principle accurately describes diffraction in the Monte Carlo ray-trace environment. This goal is achieved by systematic intercomparison of dedicated experimental, theoretical, and numerical results. We evaluate the success of the Huygens-Fresnel principle by predicting and carefully measuring the diffraction fringes produced by both single slit and circular apertures. We then compare the results from the analytical and numerical approaches with each other and with dedicated experimental results. We conclude that use of the MCRT method to accurately describe diffraction requires that careful attention be paid to the interplay among the number of aperture points, the number of rays traced per aperture point, and the number of bins on the screen. This conclusion is supported by standard statistical analysis, including the adjusted coefficient of determination, adj, the root-mean-square deviation, RMSD, and the reduced chi-square statistics, . OCIS codes: (050.1940) Diffraction; (260.0260) Physical optics; (050.1755) Computational electromagnetic methods; Monte Carlo Ray-Trace, Huygens-Fresnel principle, obliquity factor 1. INTRODUCTION here. We compare the results from the analytical and numerical approaches with each other and with the dedicated experimental The Monte Carlo ray-trace (MCRT) method has long been utilized to results. -
Three Gratings System for the Measurement of Refractive Index of Liquids
International Journal of Applied Science and Mathematics Volume 3, Issue 3, ISSN (Online): 2394-2894 Three Gratings System for the Measurement of Refractive Index of Liquids Shyam Singh Physics Department, University of Namibia Private Bag 13301, Windhoek, NAMIBIA Fax: 264-61-206-3791 Email: [email protected] Abstract – This paper describes a very exciting method of a distance x from the third grating due to the interference finding the refractive index of liquids using a three of diffracted light from the third grating. The central point transmission diffraction gratings. An especially design glass is brighter than the other two points but the other two cell is used whose width can be changed using a railing. Light points are at equidistant from the central point as can be from a low power helium-neon laser is diffracted by a seen in Fig 1. This situation confirms the perfect transmission diffraction grating and is collimated by a lens L of short focal length. The parallel beams of light are received alignment and setup of the experiment. The distance by the second grating mounted on the first wall of the glass between the walls of the glass cell d is predetermined cell and its first order diffraction is formed on the second based on the experimental liquid and this is the only wall of the glass cell. The interference is received on a screen drawback of this experiment. However, this drawback is at a distance x from the third grating mounted on the second not so crucial as the distance d can easily be adjusted by a wall of the glass cell.