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The face of a prism of refracting angle A is coated with silver. A light ray after first being incident at an angle of incidence 2A on the first face of the prism, is refracted and is then reflected from the second face, retracting its path. Calculate the value of the refractive index of the prism. |
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Answer» Solution :LET PQR be a glass prism. The refracting surface PR of the prism is coated with mercury. In the figure, INCIDENT ray DB is refracted along BC and the light ray returns following the same path getting REFLECTED from the surface PR. `therefore "" anglePCB = 90^(@)` and `anglePBC = alpha = (90^(@) - A)` `["where" angleBPC = "refracting ANGLE of the prism = A"]` Again, from the figure, `alpha + r = 90^(@)` `alpha = (90^(@) - r)` Comparing equations (1) and (2), we may write A = r `"Here", "" mu = (sini)/(sinr) = (SIN2A)/(sinA) or, mu = (2sinAcosA)/(sinA)` `or, "" mu = 2cosA` Therefore, required refractive index is 2 cos A. 
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