Halliday, Resnick & Walker — Interference: Problem 4

4 Reflection by thin layers. In Fig. 35-22, 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 $r_1$ and $r_2$ interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, problem 4 in Table 35-2 refers to the indexes of refraction $n_1 = 1.56$, $n_2 = 1.34$, and $n_3 = 1.42$, the type of interference is maximum (max), and the wavelength $\lambda$ is $587\text{ nm}$ as measured in air. Where $L$ is missing, give the second least thickness.