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Q.

A light ray is moving from denser (refractive index = $μ$ ) to air. If the angle of incidence is half the angle of refraction, find out the angle of refraction.

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a

$2 \cot^{- 1} (\frac{μ}{2})$

b

$2 \sin^{- 1} (\frac{μ}{2})$

c

$2 \cos^{- 1} (\frac{2}{μ})$

d

$2 \cos^{- 1} (\frac{μ}{2})$

answer is B.

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Detailed Solution

Given i = $\frac{r}{2}$
So, from snell's law $μ \sin i = \sin r$
$μ \sin (\frac{r}{2}) = 2 \sin (\frac{r}{2}) \cos (\frac{r}{2})$
$\cos (\frac{r}{2}) = \frac{μ}{2} \Rightarrow r = 2 \cos^{- 1} (\frac{μ}{2})$

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