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Natural light falls at the Brewster angle on the surfcae of glass. Using the Fresnel equations, find (a) the reflection coefficient, (b) the degree of polarization of refracted light. |
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Answer» Solution :From Fresnel's equations `{:(I'_(bot)=I_(bot)(sin^(2)(theta_(1)-theta_(2)))/(sin^(2)(theta_(1)+theta_(2)))),(I'_(||)=0):}}` at Brewste's angle `I'_(||) = 0` `I'_(bot) = I_(bot) sin^(2)(theta_(1) - theta_(2))` `= (1)/(2)I (sin theta_(1) COS theta_(2) - cos theta_(1) sintheta_(2))^(2)` Now `tan theta_(1) = N, sin theta_(1) = (n)/(sqrt(n^(2) + 1))` `cos theta_(1) = (1)/(sqrt(n^(2) + 1)), sintheta_(2) = cos theta_(1)` `cos theta_(2) = sin theta_(1)` `I'_(bot) = (1)/(2)I ((n^(2) - 1)/(n^(2) + 1))^(2)` Thus reflection coefficient `= RHO = (I'_(bot))/(I)` `= (1)/(2) ((n^(2) - 1)/(n^(2) + 1))^(2)0.074` on putting `n= 1.5` (b) For the REFRACTED light `I''_(bot) = I_(bot) - I'_(bot) = (1)/(2)I {1-((n^(2) - 1)/(n^(2) + 1))^(2)}` `= (1)/(2)I (4n^(2))/((n^(2) + 1)^(2))` `I'_(||) = (1)/(2)I` at the Brewster's angle. Thus the degree of polarization of the refraced light is `P = (I''_(||) - I''_(bot))/(I''_(||) + I''_(bot)) = ((n^(2) + 1)^(2)-4n^(2))/((n^(2) + 1)^(2) + 4n^(2))` `= ((n^(2) - 1)^(2))/(2(n^(2)+1)^(2) -(n^(2) -1)^(2)) = (rho)/(1-rho)` On putting `rho = 0.074` we get `P = 0.080`. |
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