Halliday, Resnick & Walker — Interference: Problem 33

33 Two waves of light in air, of wavelength \(\lambda = 600.0 \text{ nm}\), are initially in phase. They then both travel through a layer of plastic as shown in Fig. 35-26, with \(L_1 = 4.00 \mu\text{m}\), \(L_2 = 3.50 \mu\text{m}\), \(n_1 = 1.42\), and \(n_2 = 1.60\). (a) What multiple of \(\lambda\) 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?