Chapter 35, Problem 92P

Figure 35-56a shows two light rays that are initially in phase as they travel upward through a block of plastic, with wavelength 400 nm as measured in air. Light ray r₁ exits directly into air. However, before light ray r₂ exits into air, it travels through a liquid in a hollow cylinder within the plastic. Initially the height L_liq of the liquid is 40.0 μm, but then the liquid begins to evaporate. Let φ be the phase difference between rays r₁ and r₂ once they both exit into the air. Figure 35-56b shows φ versus the liquids height L_liq until the liquid disappears, with φ given in terms of wavelength and the horizontal scale set by L_s = 40.00 μm. What are (a) the index of refraction of the plastic and (b) the index of refraction of the liquid?

Figure 35-56 Problem 92.