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Consider a thin film of magnesium fluoride MgF2 (nMgF2 = 1.38) on top of a sheet of glass (n, = 1.52). Light comes in at an angle 0. Part of the light is reflected, while some light is transmitted into the film, where this light too reflects and emerges once again from the film. nair nMgF 2 It nglass Ot 1/2 Ot (a) The path difference in this situation will be determined by 72 71 - nMgF26 - nair L Find the lengths & and L as denoted in the diagram. Carefully note that L is the distance between the two points signified above, while /2 is given by the diagonal lengths the light travels in the film. Express your answer in terms of t, et, 0, common trigonometric functions and the indices of refraction. (b) Using Snell's law, express r2 - 1 in terms of t, Ot, common trigonometric functions and the indices of refraction. Simplify your expression as much as possible. (c) Given the stated indices of refraction, write the equations describing which wavelengths permit con- structive and destructive interference. Write your expression as a function of the thickness of the film t, nMgF2, 0t, A and integers m. (d) Suppose we want the thin film to act as a anti-reflecting coating at normal incidence, Or = 0, for the wavelength > = 580 nm. Given this information, what is the minimum allowed size of the thin film? (e) Suppose that the film thickness is given by the value you found above. What is the largest wavelength reflected when the incident light is instead at 0; = 45