A parallel sides glass slab of thickness 4 cm is made of a material of refractive index $\sqrt{3}$ . When light is incident on one of the parallel faces at an angle of $60^{0}$ , it emerges from the other parallel face. Find the lateral displacement of the emergent beam.

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$\frac{2}{\sqrt{3}}$

$\frac{5}{\sqrt{3}}$

$\frac{7}{\sqrt{3}}$

$\frac{4}{\sqrt{3}}$

answer is B.

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Detailed Solution

$μ = \frac{\sin i}{\sin r}$

$\sqrt{3} = \frac{s i n 60^{0}}{s i n r}; s i n r = \frac{1}{2}$

$r = 30^{0}$

Lateral shift $= \frac{t}{c o s r} s i n (i - r)$

$= \frac{4}{c o s 30^{0}} s i n (60^{0} - 30^{0})$

$= \frac{4 \sin 30^{0}}{\cos 30^{0}} = 4 \tan 30^{0}$

$= \frac{4}{\sqrt{3}}$

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