Halliday, Resnick & Walker — Interference: Problem 19

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. Problem 19 Data: $n_1 = 1.60$, $n_2 = 1.40$, $n_3 = 1.57$, Type = min, $L$ = 2nd, $\lambda = 632$