In the figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.420 nm makes an angle 0 = What is the unit cell size ao? 61.9° with the top face of the crystal. X rays ao

In the figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.420 nm makes an angle 0 = What is the unit cell size ao? 61.9° with the top face of the crystal. X rays ao

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter37: Diffraction Patterns And Polarization

Section: Chapter Questions

Problem 35AP

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A film of oil on a puddle in a parking lot shows a variety of bright colors in swirled patches. What can you say about the thickness of the oil film? (a) It is much less than the wavelength of visible light. (b) It is on the same order of magnitude as the wavelength of visible light. (c) It is much greater than the wavelength of visible light. (d) It might have any relationship to the wavelength of visible light.
A narrow beam of ultrasonic waves reflects off the liver tumor illustrated in Figure P35.26. The speed of the wave is 10.0% less in the liver than in the surrounding medium. Determine the depth of the tumor.
In each of the following situations, a wave passes through an opening in an absorbing wall. Rank the situations in order from the one in which the wave is best described by the ray approximation to the one ill which the wave coming through the opening spreads out most nearly equally in all directions in the hemisphere beyond the wall, (a) The sound of a low whistle at 1 kHz passes through a doorway 1 m wide, (b) Red light passes through the pupil of your eye. (c) Blue light passes through the pupil of your eye. (d) The wave broadcast by an AM radio station passes through a doorway 1 m wide, (e) An x-ray passes through the space between bones in your elbow Joint.
You are working as a demonstration assistant for a physics professor. For an upcoming lecture on diffraction gratings, he wishes to perform a demonstration where he shines a laser pointer at normal incidence onto the recorded surface of a DVD that is laying flat on the demonstration table. (a) He asks you to determine how many additional maxima beyond the normal reflection (which will be blocked by his hand holding the laser pointer) will be projected onto the ceiling or walls of the room if he uses a laser pointer with a wavelength of 632.8 nm. (b) He also asks you if he can show more maxima by using a laser pointer of another visible color. The tracks of pits on a DVD are separated by 0.800 m.
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Pierre de Fermat (16011665) showed that whenever light travels from one point to another, its actual path is the path that requires the smallest time interval. This statement is known as Fermats principle. The simplest example is for light propagating in a homogeneous medium. It moves in a straight line because a straight line is the shortest distance between two points. Derive Snells law of refraction from Fermats principle. Proceed as follows. In Figure P34.54, a light ray travels from point P in medium 1 to point Q in medium 2. The two points are, respectively, at perpendicular distances a and b from the interface. The displacement from P to Q has the component d parallel to the interface, and we let x represent the coordinate of the point where the ray enters the second medium. Let t = 0 be the instant the light starts from P. (a) Show that the time at which the light arrives at Q is t=r1v1+r2v2=n1a2+x2c+n2b2+(dx)2c (b) To obtain the value of x for which t has its minimum value, differentiate t with respect to x and set the derivative equal to zero. Show that the result implies n1xa2+x2=n2(dx)b2+(dx)2 (c) Show that this expression in turn gives Snells law. n1sin1=n2sin2 Figure P34.54 Problems 54 and 55.
Iridescent peacock feathers are shown in Figure P27.68a (page 938). The surface of one microscopic barbule is composed of transparent keratin that supports rods of dark brown melanin in a regular lattice, represented in Figure P27.68b. (Your fingernails are made of keratin, and melanin is the dark pigment giving color to human skin.) In a portion of the feather that can appear turquoise (blue-green), assume the melanin rods are uniformly separated by 0.25 m, with air between them. (a) Explain how this structure can appear turquoise when it contains no blue or green pigment. (b) Explain how it can also appear violet if light falls on it in a different direction. (c) Explain how it can present different colors to your two eyes simultaneously, which is a characteristic of iridescence. (d) A compact disc can appear to be any color of the rainbow. Explain why the portion of the feather in Figure P27.68b cannot appear yellow or red. (e) What could be different about the array of melanin rods in a portion of the feather that does appear to be red? Figure P27.68 (a) Iridescence in peacock feathers. (b) Microscopic section of a feather showing dark melanin rods in a pale keratin matrix.