In the given situation, for what value of `i`, the incidence ray will retrace its initial path.

Options

A. `cos^(-1)[mu_(1)sin((pi)/(4)-sin^(-1)(mu_(2))/(sqrt(2)mu_(1)))]`
B. `sin^(-1)[mu_(1)sin((pi)/(4)-sin^(-1)(mu_(2))/(sqrt(2)mu_(1)))]`
C. `sin^(-1)[mu_(2)sin((pi)/(4)-sin^(-1)(mu_(1))/(sqrt(2)mu_(2)))]`
D. `cos^(-1)[mu_(2)sin((pi)/(4)-sin^(-1)(mu_(1))/(sqrt(2)mu_(2)))]`

Answer

B

Explanation

Since incident ray retraces its path it must strike the plane mirror perpendicularly.
From Snell's law `sini=mu_(1)sinr_(1)`
and `mu_(1)sinr_(2)=mu_(2)sin45^(@)impliesmu_(1)sinr_(2)=(mu_(2))/(sqrt(2))`
`impliesr_(2)=sin^(-1)((mu_(2))/(sqrt(2)mu_(1)))`
Also `r_(1)+r_(2)=(pi)/(4)`
`becauser_(1)=(pi)/(4)-sin^(-1)((mu_(2))/(sqrt(2)mu_(1)))`
`becausei=sin^(-1)[mu_(1)sin((pi)/(4)-sin^(-1)(mu_(2))/(sqrt(2)mu_(1)))]`