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$\bullet$X-ray diffraction of salt. X rays with a wavelength of0.125 $\mathrm{nm}$ are scattered from a cubic array (of a sodium chlo-ride crystal), for which the spacing of adjacent atoms is$a=0.282 \mathrm{nm}$ (a) If diffraction from planes parallel to a cubeface is considered, at what angles $\theta$ of the incoming beam relativeto the crystal planes will maxima be observed? (b) Repeat part(a) for diffraction produced by the planes shown in Fig.$26.33 \mathrm{a},$ which are separated by $a / \sqrt{2} .$

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a) $12.8^{\circ}$, $26.3^{\circ}$, $41.7^{\circ}$, $62.4^{\circ}$b) $18.3^{\circ}$, $38.8^{\circ}$, $70.1^{\circ}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

University of Winnipeg

Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

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X-Ray Diffraction of Salt.…

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A beam of x-rays of wavele…

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In Fig. $36-30$, let a be…

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In Fig. $36-48$, let a bea…

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In Fig. $36-48,$ let a bea…

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The atomic planes in a cry…

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In Fig. 37-36, let a beam …

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X rays with a wavelength o…

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The structure of the NaCl …

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When salt is sprinkled on …

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A beam of X-rays of wavele…

01:20

02:45

When X-rays of wavelength …

00:51

In their study of X-ray di…

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A parallel beam of X-rays …

00:50

Okey dokey. In this problem, we're dealing with X ray diffraction. So the wavelength of our X rays that were shining in 0.125 near the meters, The spacing of our atoms. 0.28 to Nana meters. And for part A. We want to know at what angles are we going to see? Constructive Maxima. When are light is hitting the cube straight on. So if this is our beautiful cube, that's hideous. Sorry of Adams. My light is coming in this way. Okay, so I bragged. A fraction occurs when two D signed data musical toe end, Lambda and D is the spacing between the plains of Adam's. So impart a The spacing between our planes of Adams is just the distance between the atoms. So, up here, my d is just a rights. Now we're gonna solve for theta. So if we divide to a over here, then we can take the ember sign on land over to a Okay, So its inverse sine of end lamb does my 0.1 to 5 nano meters and a kiss. The spacing of my eye. Adams. Okay, so if I plug in and um equals one, we get angles of 12.8 degrees for a maximum flowing in chemicals to be a 26.3 degrees, um, equals three for you, 1.7 degrees and m equals for me. Get 62.4 degrees similarly for part B. Now, the spacing between my claims is a over route too. So my angle lambda over to D becomes too, eh? Over route, too. So for M equals one, that's 18.3 degrees, um, equals two 38.8 degrees and then my equals three 70.1.

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