Quarter part of a transparent cylinder ABC of radius R is kept on a horizontal floor and a horizontal beam of light falls on the cylinder in the two different arrangement of cylinder as shown in figure (a) & (b) . In arrangement (a) light converges at point D , which is at a distance 2R/m from B. And in arrangement (b) light converges at point E, which is at a distance R/(m-1) from C. Find out the refractive index of the material.

Answer

A

Explanation

For case (a) `(mu)/(v_(1)) - (1)/(oo) = (mu-1)/(R), (1)/(v_(2))- (mu)/(v_(1) - R) = (1-mu)/(oo) "and" v_(2) = (2R)/(m) implies m=2(mu-1)mu`
For case(b) `(1)/(v_(2))- (mu)/(oo) = (1-mu)/(-R) "and" v_(2) = (R)/(m-1) implies mu=m`
Therefore `mu= 2 (mu-1) mu implies mu-1 = (1)/(2) implies mu = 1.5`