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Question

A ray of light travelling in air is incident at angle of 30 on one surface of a slab in which refractive index varies with y. The light travels along the curve y=4x2 (y and x are in metre) in the slab. If the refractive index of the slab at y=12 m in the slab is 15xo, then xo is

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Solution


By snell's law at incidence and at y
1×sin30=n sin i
where n is Refractive index at y and i is angle of incidence at y.

Now from slope
tan(90i)=dydx=8x=4y
cot i=4y=412=22
sin i=13n=sin 30osin i=1213=1.5

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