A ray of light travelling in air is inciden at angle of inciden `30^@` on one surface of slab in which refractive index varies with y. The light travels along the curve `y =4x^(2)` ( y and x are in meter) in the slab. Find out the refractive index of the slab at `y=1//2m` in the slab.

Explanation

Let R.I. at `y=y` is `mu` and corresponding angle of refraction is `theta`
`musintheta=1sin30^@` (i)
and `tan((pi)/(2)-theta)=(dy)/(dx)rArrcottheta=8xrArr cottheta=(8y^(1//2))/(2)`
`cot theta=4 y^(1//2)`
At `y=1//2mrArrcottheta=(4)/(sqrt(2))=2sqrt(2)` or `sintheta=(1)/(2)`
From (i), `muxx(1)/(3)=(1)/(2)rArrmu=(3)/(2)`