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Using the Fresnel equations, find: (a) the reflection coefficient of natural light falling normally on the surface of glass, (b) the relative loss of luminous flux due to reflections of a paraxial ray of natural light passing through an aligned aoptical system comprising five glass lenses (secondary reflections o flight are to be neglected). |
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Answer» Solution :We decompose the natural light into two components with intensity `I_(||) = (1)/(2)I_(0) = I_(bot)` where `||` has its electirc vector OSCILLATING parallel to the PLANE of incidence and `bot` has the same `bor^(r )` to it. By Frensel's equations for normal incidence `(I'_(bot))/(I_(bot)) = underset(theta_(1)rarr0)lim (sin^(2)(theta_(1) - theta_(2)))/(sin^(2)(theta_(1) + theta_(2))) = underset(theta_(1)rarr0)lim ((theta_(1) - theta_(2))/(theta_(1) + theta_(2)))^(2) = ((n - 1)/(n + 1))^(2) = rho` similarly `(I'_(||))/(I_(||)) = rho = ((n - 1)/(n + 1))^(2)` Thus `(I')/(I) = rho = ((0.5)/(2.5))(2) = (1)/(25) = 0.04` (b) The REFLECTED light at the first surface has the intensity `I_(1) = rhoI_(0)` Then the transmitted light has the intensity `I_(2) = (1-rho)I_(0)` At the second surface where light emerges form glass inot air, the reflection coefficient is again `rho` because `rho` is invariant under the subsitution `n rarr (1)/(n)`. Thus `I_(3) = rho(1 - rho)I_(0)` and `I_(4) = (1 - rho)^(2) I_(0)`. For `N` lenses the loss in luminous FLUX is then `(Delta Phi)/(Phi) = 1- (1- rho)^(2N) = 0.335` for `N = 5` 
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