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A ray of light from a denser medium strikes a rarer medium. The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are $r$ and $r^{1}$ . The critical angle would be

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$\sin^{- 1} (\tan r)$

$\tan^{- 1} (\sin r)$

$s i n^{- 1} (\tan r^{1})$

$\tan^{- 1} (\sin r^{1})$

answer is A.

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Detailed Solution

$\frac{μ_{r}}{μ_{d}} = \frac{S i n i}{S i n r^{1}}$ $(\begin{matrix} r + r^{1} = 90 ° \\ r^{1} = 90 ° - r \\ i = r \end{matrix})$

$\frac{μ_{r}}{μ_{d}} = \frac{S i n r}{S i n (90 ° - Ω)} = \frac{S i n r}{C o s r} = \tan r$

SinC = $\frac{μ_{r}}{μ_{d}}$

$S i n C = \tan r$

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