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Chapter 35: Q17P (page 1075)
In Fig. 35-37, two radio frequency point sources and , separated by distance , are radiating in phase with . A detector moves in a large circular path around the two sources in a plane containing them. How many maxima does it detect?
The total number of the maxima is 16.
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Reflection by thin layers. In Fig. 35-42, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays and interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35- 2 refers to the indexes of refraction , and , the type of interference, the thin-layer thickness in nanometres, and the wavelength in nanometres of the light as measured in air. Where is missing, give the wavelength that is in the visible range. Where localid="1663142040666" is missing, give the second least thickness or the third least thickness as indicated
In Fig. 35-38, sourcesand emit long-range radio waves of wavelength , with the phase of the emission from ahead of that from source Bby .The distance from Ato detector Dis greater than the corresponding distance localid="1663043743889" by .What is the phase difference of the waves at D ?
Reflection by thin layers. In Fig. 35-42, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) The waves of rays and interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35- 2 refers to the indexes of refraction , and, the type of interference, the thin-layer thickness in nanometres, and the wavelength in nanometres of the light as measured in air. Where is missing, give the wavelength that is in the visible range. Where is missing, give the second least thickness or the third least thickness as indicated.
In Fig, monochromatic light of wavelength diffracts through narrow slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane through the focal point of the lens, screen A is effectively very distant. The lens plays no other role in the experiment and can otherwise be neglected.) Light travels from the slit directly to A interferes with light from the slit that reflects from the mirror to A. The reflection causes a half-wavelength phase shift. (a) Is the fringe that corresponds to a zero path length difference bright or dark? Find expressions (like Eqs. 35-14 and 35-16) that locate (b) the bright fringes and (c) the dark fringes in the interference pattern. (Hint: Consider the image of S produced by the minor as seen from a point on the viewing screen, and then consider Young’s two-slit interference.)
In Figure 35-50, two isotropic point sources and emit light in phase at wavelength and at the same amplitude. The sources are separated by distance on an x axis. A viewing screen is at distance from and parallel to the y axis. The figure shows two rays reaching point P on the screen, at height . (a) At what value of do the rays have the minimum possible phase difference? (b) What multiple of gives that minimum phase difference? (c) At what value of do the rays have the maximum possible phase difference? What multiple of gives (d) that maximum phase difference and (e) the phase difference when ? (f) When , is the resulting intensity at point P maximum, minimum, intermediate but closer to maximum, or intermediate but closer to minimum?
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