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

Explanation

(a). `1xxsin30^(@)=nsini`
`sini=(1)/(2n)`
`tani=(1)/(sqrt(4n^(2)-1))`
`(dy)/(dx)=(1)/(sqrt(x+3))`
`int_(0)^(y)dy=int_(0)^(x)(x+3)^(-1//2)dx`
`y=2(sqrt(1+3)-sqrt(3))" "y=2(2-sqrt(3))`
`therefore` position at which ray comes out of the medium is `(1,2(2-sqrt(3)))`