The refractive index of the medium with a certain region, x > 0, y > 0, changes with y. A thin light ray travelling in the x-direction in medium having refractive index $μ_{0} = 1$ strikes another medium of refractive index $μ$ at right angles and moves through the medium along a circular arc of radius R as shown in the figure. The material with the greatest known refractive index is diamond, but even the refractive index of this material does not reach the value $μ_{\max}$ = 2.5. It is this limit that sets the maximum angular size of the arc the light ray can cover. Angular size of arc is the angle subtendly by the arc at the centre.

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Infinity Learn · Accepted Answer

The variant of refractive index $μ$ with y is given as $μ = \frac{R}{R - y}$

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If the maximum angular size of the arc of light is $θ_{\max}$ then $\sin θ_{\max} = 2 / 5$

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If the maximum angular size of the arc of light is $θ_{\max}$ then $\cos θ_{\max} = 2 / 5$

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