64, 65 59 Transmission through thin layers. In Fig. 35-43,

Chapter , Problem 57

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64, 65 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 n1, n2, and n3, the type SSM SSM WWW ! Figure 35-43 57 through 68. n1 n2 n3 L r3 i r4 Table 35-3 57 through 68: Transmission Through Thin Layers. See the setup for these problems. n1 n2 n3 Type L l 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 of interference, the thin-layer thickness L in nanometers, and the wavelength l in nanometers of the light as measured in air. Where l 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.

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