Two transparent media $A$ and $B$ are separated by a plane boundary. The speed of light in medium $A$ is $2.0 \times 10^{8} m s^{- 1}$ and in medium $B$ is $2.5 \times 10^{8} m s^{- 1}$ . The critical angle for which a ray of light going from $A$ to $B$ is totally internally reflected is

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

$\sin^{- 1} (\frac{2}{5})$

$\sin^{- 1} (\frac{4}{5})$

$\sin^{- 1} (\frac{3}{4})$

answer is C.

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Detailed Solution

Refractive index of medium $A$ with respect to medium $B$ is

$μ = \frac{2.5 \times 10^{8}}{2.0 \times 10^{8}} = \frac{5}{4}$

For total internal reflection

$\sin i_{C} = \frac{1}{μ} = \frac{4}{5}$

$\Rightarrow i_{C} = \sin^{- 1} (\frac{4}{5})$

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