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A rod of glass $(μ = 1 .5)$ and of square cross section is bent into the shape shown in figure. A parallel beam of light falls on the plane flat surface A as shown in figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of $\frac{d}{R}$ light entering the glass slab through surface A emerges from the glass through B ?

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1.3

1.5

0.5

None of these

answer is B.

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Detailed Solution

All of the rays from surface A will reach the surface B only if all of the light rays under go total internal reflection.

$\sin C = \frac{R}{R + d}$

$\frac{1}{μ} = \frac{R}{R + d} \Rightarrow 1 + \frac{d}{R} = \frac{3}{2}$

$\Rightarrow \frac{d}{R} = 0 .5$

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