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Chapter 35: Q29P (page 1076)
Two waves of the same frequency have amplitudes 1.00 and 2.00. They interfere at a point where their phase difference is 60.0掳. What is the resultant amplitude?
The resultant amplitude of wave is 2.65 .
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In Fig. 35-39, two isotropic point sources S1 and S2 emit light in phase at wavelength and at the same amplitude. The sources are separated by distance . They lie on an axis that is parallel to an x axis, which runs along a viewing screen at distance . The origin lies on the perpendicular bisector between the sources. The figure shows two rays reaching point P on the screen, at position. (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 ofdo 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?
In Fig. 35-45, a broad beam of monochromatic light is directed perpendicularly through two glass plates that are held together at one end to create a wedge of air between them. An observer intercepting light reflected from the wedge of air, which acts as a thin film, sees 4001 dark fringes along the length of the wedge. When the air between the plates is evacuated, only 4000 dark fringes are seen. Calculate to six significant figures the index of refraction of air from these data.
Figure 35-30 shows three situations in which two rays of sunlight penetrate slightly into and then scatter out of lunar soil. Assume that the rays are initially in phase. In which situation are the associated waves most likely to end up in phase? (Just as the Moon becomes full, its brightness suddenly peaks, becoming 25% greater than its brightness on the nights before and after, because at full Moon we intercept light waves that are scattered by lunar soil back toward the Sun and undergo constructive interference at our eyes. Before astronauts first landed on the Moon, NASA was concerned that backscatter of sunlight from the soil might blind the lunar astronauts if they did not have proper viewing shields on their helmets.)
In Fig. 35-31, a light wave along ray reflects once from a mirror and a light wave along ray reflects twice from that same mirror and once from a tiny mirror at distance from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength 620 nm and are initially in phase. (a) What is the smallest value of that puts the final light waves exactly out of phase? (b) With the tiny mirror initially at that value of , how far must it be moved away from the bigger mirror to again put the final waves out of phase?
In Fig. 35-45, two microscope slides touch at one end and are separated at the other end. When light of wavelength 500 nm shines vertically down on the slides, an overhead observer sees an interference pattern on the slides with the dark fringes separated by 1.2 mm. What is the angle between the slides?
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