A light ray enters into a medium whose refractive index varies along the x-axis as `n(x) = n_(0) sqrt(1+(x)/(4))` where `n_(0)=1`. The medium is bounded by the plates `x =0,x =1` & `y =0`. It the ray enters at the origin at an angle `30^(@)` with x-axis

Options

A. equation of trajectory of the light ray is `y =[sqrt(3 +x) - sqrt(3)]`
B. equation of trajectory of the light ray is `y = 2[sqrt(3 + x)- sqrt(3)]`
C. the coordinate the point at which light ray comes out from the medium is `[1,2(2- sqrt(3))]`
D. the coordinate the point at which light ray comes out from the medium is `[0,2(2- sqrt(3))]`

Answer

B, C

Explanation

`1 xx sin 30^(@) = n sin i`
`sin i =(1)/(2n) rArr tan i(1)/(sqrt(4n^(2)-1))`
`(dy)/(dx)=(1)/(sqrt(x+3))rArr underset(0) overset(l) (int) dy = underset(0)overset(x)(int)(x+3)^(1//2)dx`
`y = (sqrt(x+3)-sqrt(3))`
(b) When x = 1
`y = 2 (sqrt(1 + 3)- sqrt(3))`
`y = 2(2- sqrt(3))`
`:.` Position at which ray comes out of the medium is `(1,2(2- sqrt(3))`