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The critical angle for refraction from medium -1 to air is $θ_{1}$ and that from medium - 2 to air is $θ_{2}$ . If medium -2 is denser than medium -1. Find the critical angle for refraction from medium - 2 to medium.

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$\sin^{- 1} (\frac{\sin θ_{2}}{\sin θ_{1}})$

$\sin^{- 1} (\frac{\sin θ_{1}}{\sin θ_{2}})$

$\sin^{- 1} (\sin θ_{2})$

$\sin^{- 1} (\sin θ_{1})$

answer is A.

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Detailed Solution

$\begin{array}{l} μ_{1} = \frac{1}{\sin θ_{1}}, μ_{2} = \frac{1}{\sin θ_{2}} \\ \frac{μ_{1}}{μ_{2}} = \sin θ \Rightarrow \frac{\sin θ_{2}}{\sin θ_{1}} = \sin θ; θ = \sin^{- 1} [\frac{\sin θ_{2}}{\sin θ_{1}}] \end{array}$

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