A ray of light in air is incident at angle of incident `30^(@)` on one surface of slab in which refractive index varies with y-axis. Light travels along the curve `y=4x^(2)` in the slab. If refractive index of the slab at `y=(1)/(2)m` in the slab is `(alpha)/(2)` find `alpha`.

Answer

3

Explanation

`1xxsin30^(@)=musintheta` .(1)
`tan((pi)/(2)-theta)="slope"=(dy)/(dx)impliescottheta=8x=8((y)/(4))^((1)/(2))`

`cottheta=4sqrt(4)` ltbtgt at `y=(1)/(2)impliescottheta=(4)/(sqrt(2))=2sqrt(2)impliesintheta=(1)/(3)`
from (1) `implies1xx(1)/(2)=muxx(1)/(3)impliesmu=(3)/(2)`
`alpha=3`