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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$2 \cos^{- 1} (\frac{2}{μ})$

$2 \cos^{- 1} (\frac{μ}{2})$

$2 \sin^{- 1} (\frac{μ}{2})$

$2 \cot^{- 1} (\frac{μ}{2})$

answer is B.

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Detailed Solution

Given $i = \frac{r}{2}$

So, from snell’s law

$\begin{array}{l} μsini = sinr \\ μsin (\frac{r}{2}) = 2 \sin (\frac{r}{2}) \cos (\frac{r}{2}) \\ \cos (\frac{r}{2}) = \frac{μ}{2} \Rightarrow r = 2 \cos^{- 1} (\frac{μ}{2}) \end{array}$

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