A ray hits the y-axis making an angle `theta` with y-axis as shown in the figure. The variation of refractive index with x-coordinate is `mu=mu_0 (1-(x)/(d))` for `0lt=xlt=d(1-(1)/(mu_0))` and `mu=mu_0` for `x lt 0`, where d is a positive constant. The maximum x-coordinate of the path traced by the ray is

Options

A. `d(1-sin theta)`
B. `d(1 - cos theta)`
C. `d sin theta`
D. `d cos theta`

Answer

B

Explanation

Snell's law `= mu_(0) sin (90^(@) -0)`
`=mu_(0)(1-(x)/(d))sin 90^(@) rArr (1-(x)/(d))= cos theta`
`rArr x =d(1- cos theta)`.