Halliday, Resnick & Walker — Interference: Problem 12

1 through 12 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, each problem in Table 35-2 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. Problem 12 Given Values: Index of refraction of material 1 (\( n_1 \)): \( 1.74 \) Index of refraction of material 2 (\( n_2 \)): \( 1.59 \) Index of refraction of material 3 (\( n_3 \)): \( 1.50 \) Interference type: minimum (min) Thickness of layer 2 (\( L \)): \( 415 \text{ nm} \)