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A ray of light travelling in air is inc...

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.

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The correct Answer is:
3
`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`
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