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A plane monochromatic light wave of intensity I_(0)falls normally on a plane-parallel plate both of whose surfaces have a reflection coeffiecient rho. Taking into account multiple reflections, find the intensity of the transmitted light if (a) the plate is perfectly transparent, i.e the absorption is absent, (b) teh coefficient of linear absorption is equal to x, and the plate thickness is d. |
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Answer» Solution :The multiple reflections are shown below. TRANSMISSION GIVEN a factor `(1- rho)` while reflections given factors of `rho`. Thus the TRANSMITTED intensity assuming inchoheren LIGHT is `(1 - rho)^(2) I_(0) + (1- rho)^(2)rho^(2)I_(0) + (1-rho)^(2)rho^(4)I_(0)+..` `= (1- rho)^(2)I_(0) (1+rho^(2) +rho^(4) + rho^(6)+...)` `= (1 - rho)^(2) I_(0) xx (1)/(1 - rho^(2)) = I_(0) (1-rho)/(1+ rho)`. (b) When there is ABSORPTION, we pick up a factor `sigma = e^(-chid d)` in each traversal of the plane. Thus we get `(1 - rho)^(2)sigmaI_(0) + (1- rho)^(2) sigma^(3) rho^(2)I_(0) + (1 - rho)^(2) sigma^(5) rho^(4)I_(0) +....` `= (1- rho)^(2) sigmaI_(0) (1 + sigma^(2) rho^(2) + sigma^(4) rho^(4) + ....)` `= I_(0) (sigma(1 - rho)^(2))/(1 - sigma^(2) rho^(2))` 
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