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Chapter 36: Q2P (page 1108)
What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at ?
The ratio of the slit width to wavelength is .
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Consider a two-dimensional square crystal structure, such as one side of the structure shown in Fig. 36-28a.The largest interplanar spacing of reflecting planes is the unit cell size . Calculate and sketch the (a) second largest, (b) third largest, (c) fourth largest, (d) fifth largest, and (e) sixth largest interplanar spacing. (f) Show that your results in (a) through (e) are consistent with the general formula
where h and k are relatively prime integers (they have no common factor other than unity).
Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by and .The fourth order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width , what are the (c) largest, (d) second largest, and (e) third largest values of the order of the maxima produced by the grating?
The wall of a large room is covered with acoustic tile in which small holes are drilled from centre to centre. How far can a person be from such a tile and still distinguish the individual holes, assuming ideal conditions, the pupil diameter of the observer鈥檚 eye to be , and the wavelength of the room light to be ?
At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer鈥檚 eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?
A circular obstacle produces the same diffraction pattern as a circular hole of the same diameter (except very near u 0).Airborne water drops are examples of such obstacles. When you see the Moon through suspended water drops, such as in a fog, you intercept the diffraction pattern from many drops. The composite of the central diffraction maxima of those drops forms a white region that surrounds the Moon and may obscure it. Figure 36-43 is a photograph in which the Moon is obscured. There are two faint, colored rings around the Moon (the larger one may be too faint to be seen in your copy of the photograph). The smaller ring is on the outer edge of the central maxima from the drops; the somewhat larger ring is on the outer edge of the smallest of the secondary maxima from the drops (see Fig. 36-10).The color is visible because the rings are adjacent to the diffraction minima (dark rings) in the patterns. (Colors in other parts of the pattern overlap too much to be visible.) (a) What is the color of these rings on the outer edges of the diffraction maxima? (b) The colored ring around the central maxima in Fig. 36-43 has an angular diameter that is 1.35 times the angular diameter of the Moon, which is 0.50掳. Assume that the drops all have about the same diameter. Approximately what is that diameter?
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