91Ó°ÊÓ

In Fig 35-59, an oil drop ($\mathit{n}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{20}$) floats on the surface of water ($\mathbf{n}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{33}$) and is viewed from overhead when illuminated by sunlight shinning vertically downward and reflected vertically upward. (a) Are the outer (thinnest) regions of the drop bright or dark? The oil film displays several spectra of colors. (b) Move from the rim inward to the third blue band and using a wavelength of 475 nm for blue light, determine the film thickness there. (c) If the oil thickness increases, why do the colors gradually fade and then disappear?

In Fig. 35-34, a light ray is an incident at angle ${\mathit{θ}}_{\mathbf{1}}\mathbf{=}\mathbf{50}\mathbf{°}$on a series of five transparent layers with parallel boundaries. For layers 1 and 3 , ${\mathit{L}}_{\mathbf{1}}\mathbf{=}\mathbf{20}\mathbf{}\mathit{μ}\mathit{m}$ , ${\mathit{L}}_{\mathbf{2}}\mathbf{=}\mathbf{25}\mathbf{}\mathit{μ}\mathit{m}$, ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{6}$and ${\mathit{n}}_{\mathbf{3}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{45}$. (a) At what angle does the light emerge back into air at the right? (b) How much time does the light take to travel through layer 3?

Figure 35-27a shows the cross-section of a vertical thin film whose width increases downward because gravitation causes slumping. Figure 35-27b is a face-on view of the film, showing four bright (red) interference fringes that result when the film is illuminated with a perpendicular beam of red light. Points in the cross section corresponding to the bright fringes are labeled. In terms of the wavelength of the light inside the film, what is the difference in film thickness between (a) points a and b and (b) points b and d?

Suppose that the two waves in Fig. 35-4 have a wavelength $\mathit{λ}\mathbf{=}\mathbf{500}\mathbf{\text{nm}}$in air. What multiple of $\mathit{λ}$gives their phase difference when they emerge if (a) ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{50}$, ${\mathit{n}}_{\mathbf{2}}\mathbf{=}\mathbf{16}$and $\mathit{L}\mathbf{}\mathbf{=}\mathbf{}\mathbf{8}\mathbf{.}\mathbf{50}\mathit{μ}\mathit{m}$; (b) ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{62}$, ${\mathit{n}}_{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{72}$, and $\mathit{L}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{50}\mathit{μ}\mathit{m}$; and (c) ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{59}$, ${\mathit{n}}_{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{79}$, and $\mathit{L}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{25}\mathit{μ}\mathit{m}$? (d) Suppose that in each of these three situations, the waves arrive at a common point (with the same amplitude) after emerging. Rank the situations according to the brightness the waves produce at the common point.

In Fig. 35-35, two light rays go through different paths by reflecting from the various flat surfaces shown.The light waves have a wavelength of 420.0 nm and are initially in phase. What are the (a) smallest and (b) second smallest value of distance L that will put the waves exactly out of phase as they emerge from the region?

Figure 35-29 shows the transmission of light through a thin film in the air by a perpendicular beam (tilted in the figure for clarity). (a) Did ray${\mathit{r}}_{\mathbf{3}}$undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phase shift for ray${\mathit{r}}_{\mathbf{4}}$? (c) If the film thickness is L, what is the path length difference between rays${\mathit{r}}_{\mathbf{3}}$and${\mathit{r}}_{\mathbf{4}}$?

Two waves of light in air, of wavelength $\mathit{λ}\mathbf{=}\mathbf{600}\mathbf{.}\mathbf{0}\mathbf{\text{nm}}$, are initially in phase. They then both travel through a layer of plastic as shown in Fig. 35-36, with ${\mathit{L}}_{\mathbf{1}}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{}\mathit{μ}\mathit{m}$, ${\mathit{L}}_{\mathbf{2}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{50}\mathbf{}\mathit{μ}\mathit{m}$, ${\mathit{n}}_{\mathbf{1}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{40}$, ${\mathit{n}}_{\mathbf{2}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{60}$and. (a) What multiple of $\mathit{λ}$gives their phase difference after they both have emerged from the layers? (b) If the waves later arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive,or intermediate but closer to fully destructive?

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 a double-slit arrangement the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits. (a)What is the angular separation in radians between the central maximum and an adjacent maximum? (b) What is the distance between these maxima on a screen 50 cm from the slits?