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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 2.74 cm and the index of refraction of the polymer is n = 1.53, how thick would you make the coating? (Assume that the index of refraction of the plane is higher than that of the coating. Also assume that the radar waves are normal to the surface of the coating. Give the minimum thickness that would make the airplane invisible to radar.) Step 1 The concept of an antireflective coating is to produce destructive interference in the waves reflecting from the first and second surfaces of the coating. If we assume the refractive index of the polymer is less than that of the material making up the body of the airplane, waves reflecting from both surfaces of the coating will experience phase reversals or 180° phase shifts. As shown in the diagram, the reversal at one surface offsets the reversal at the other surface. phase reversal -phase reversal m= 0, 1, 2,... The net path difference in the two reflected waves is 6 = 2t, where t is the thickness of the film. For destructive interference, this path difference should equal an odd number of half wavelengths in the film, 2. = 1/n, where n is the index of refraction of the polymer, 2 the wavelength of the radar, and in the resulting wavelength in the polymer film. Thus we require that 2 = (m + +), = (m + 2)(4) + = + where the order number m = 0, 1, 2,... . For the thinnest coating meeting this condition, m = 0. The required thickness for this coating is cm. 4n Submit | Skip (you cannot come back)