One face of a prism with a-refractive angle of `30^(@)` is coated with silver.A ray incident on another face at an angle of `45^(@)` is refracted and reflected from the silver coated face and retraces its path. What is the refractive index of the prism?

Explanation

Given `A=30^@ , i_1 = 45^@ and r_2 =0`
since ` , r_1 +r_2 = A`
` therefore r_1 =A =30 ^@`
Now refractive index of the prism,
`mu = ( sin i_1)/( sin r_1) = ( sin 45^@ )/(sin 30^@ ) = ((1)/(sqrt2))/(1/2) = sqrt(2)`