Chapter 35, Problem 67P

57 through 68 GO 64, 65 SSM 59 Transmission through thin layers In 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 r₃ (the light does not reflect inside material 2) and r₄ (the light reflects twice inside material 2). The waves of r₃ and r₄ 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 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 Problem 57 through 68.

Table 35-3 Problems 57 through 68: Transmission Through Thin Layers. See the setup for these problems.

	n1	n2	n3	Type	L	λ
57	1.55	1.60	1.33	min	285
58	1.32	1.75	1.39	min	3rd	382
59	1.68	1.59	1.50	max	415
60	1.50	1.34	1.42	max	380
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
66	1.60	1.40	1.80	max	200
67	1.50	1.34	1.42	min	2nd	587
68	1.55	1.60	1.33	min	3rd	612