Question

Problem 4: Dielectric coating (25 points) air dielectric glass no-1 A thin coating of dielectric material is deposited onto the sur- o face of a glass lens, so that light entering the lens first goes through an air- dielectric interface before going through a dielectric-glass interface and then into the glass. The index of refraction of air is no (which you can set to 1.) The di- electric is ni, and the glass is n2. You can assume that all μ's equal μ0, and that the incoming light is polarized in the r direction. By matching the appropriate boundary condi- tions for all wave vectors shown in the drawing, show that the transmission coefficient for light of frequency w entering the lens material is given by IR nin where d is the thickness of the dielectric layer. Note you will need to use the fact that T-β ET/E0P. with β n2/no, and should prove this expression as correct as part of your solution

Answer 1

Given that A thin coating of dielectric material is deposited onto the surface T = 4n_2/(1 + n_2)^2 + 1/n_1^2 (1 - n_1^2 (n_2^2 - n_1^2) sin^2 (n_1 wd/c) To maximize the transmission, Let us see what are the free parameters that are available n_2 = 1.5 is the referable index of glass, and is given w/c = 2pi/lambda is just the wave number and cannot be varied n_1: variable d: thickness of the dielectric layer is also variable Thus if, we minimize the denominator we can get maximum transmission since n_2 is fixed, we need to minimize the second term in the denominator minimum (1/n_1^2 (1 - n_1^2)(n_2^2 - n_1^2) sin^2 (n_1 wd/c)) \r\n will determine n_1 and d since sin^2 is positive definite, we can maximum by choosing n_1 wd/c = (2m + 1) pi/2 m = 0, 1, 2... d = (2m + 1) lambda/4n_1) with this choice, we need to minimize f(n_1) = 1/n_1^2 (1 - n_1^2)