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Chapter 36: Q94P (page 1115)
A diffraction grating 1.00 cm wide has 10 000 parallel slits. Monochromatic light that is incident normally is diffracted through 30° in the first order. What is the wavelength of the light?
The wavelength of light is 500 nm.
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A diffraction grating illuminated by monochromatic light normal to the grating produces a certain line at angle . (a) What is the product of that line’s half-width and the grating’s resolving power? (b) Evaluate that product for the first order of a grating of slit separation 900 nm in light of wavelength 600 nm.
In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelengthmakes an angle with the top face of the crystal. What is the unit cell size?
(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating Eq. 36-5 with respect to a and equating the result to zero, obtaining the condition . To find values of a satisfying this relation, plot the curve and the straight line and then find their intersections, or use calculator to find an appropriate value of a by trial and error. Next, from , determine the values of associated with the maxima in the singleslit pattern. (These m values are not integers because secondary maxima do not lie exactly halfway between minima.) What are the (b) smallest and (c) associated , (d) the second smallest (e) and associated , (f) and the third smallest (g) and associated ?
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°. Assume that the drops all have about the same diameter. Approximately what is that diameter?
In a double-slit experiment, the slit separation d is 2.00 times the slit width w. How many bright interference fringes are in the central diffraction envelope?
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