55. Alice directs a beam of 0.12 nm x rays at certain planes of a silicon crystal. As she increases the angle of incidence of the beam from zero, the first strong interference maximum occurs when the beam makes an angle of θ = tan⁻¹() with the planes. How far apart are the planes? (A) 0.045 nm (B) 0.075 nm (C) 0.1 nm (D) 0.15 nm (E) 0.2 nm

57. A thin layer of oil with an index of refraction n = 1.5 coats a glass plate with an index of refraction of 1.8. White light from air (n = 1.0) is incident normal to the film. In the reflected light: (1) Fully constructive interference occurs at a wavelength of λ₁ = 600 nm. (2) Fully destructive interference occurs at a wavelength of λ₂ = 400 nm. Assume that both wavelengths correspond to the same interference order, what is the thickness of the oil film? (A) 100 nm (B) 133 nm (C) 167 nm (D) 200 nm (E) 266 nm

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