Chapter 35, Problem 62P

Fig. 35-43, 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 ${\mathrm{r}}_3$ (the light does not reflect inside material 2) and ${\mathrm{r}}_4$ (the light reflects twice inside material 2). The waves of ${\mathrm{r}}_3$ and ${\mathrm{r}}_4$ 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 ${\mathrm{n}}_1$, ${\mathrm{n}}_2$, and ${\mathrm{n}}_3$, the type of interference, the thin-layer thickness L in nanometers, and the wavelength 𝛌 in nanometers of the light as measured in air. Where 𝛌 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.

Figure 35-45

	${\mathrm{n}}_1$	${\mathrm{n}}_2$	${\mathrm{n}}_3$	Type	L	𝛌
61	1.32	1.75	1.39	Min	325
62	1.68	1.59	1.50	Max	2nd	342
63	1.40	1.46	1.75	Max	2nd	482
64	1.40	1.46	1.75	Max	210
65	1.60	1.40	1.80	Min	2nd	632

Table 35-3: Transmission Through Thin Layers.