Chapter 35, Problem 61P

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 35-43

Table 35-3: Transmission Through Thin Layers.

	${\mathrm{n}}_1$	${\mathrm{n}}_2$	${\mathrm{n}}_3$	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