Halliday, Resnick & Walker — Interference: Problem 20

13 through 24 Transmission through thin layers. In Fig. 35-23, 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.) Part of the light ends up in material 3 as ray \(r_3\) (the light does not reflect inside material 2) and \(r_4\) (the light reflects twice inside material 2). The waves of \(r_3\) and \(r_4\) interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction \(n_1\), \(n_2\), and \(n_3\), the type of interference, the thin-layer thickness \(L\) in nanometers, and the wavelength \(\lambda\) in nanometers of the light as measured in air. Where \(\lambda\) is missing, give the wavelength that is in the visible range. Where \(L\) is missing, give the second least thickness or the third least thickness as indicated. Data for Problem 20: \(n_1 = 1.32, n_2 = 1.78, n_3 = 1.39\), Type = min, \(L\) = 3rd, \(\lambda = 382 \text{ nm}\).