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A ray of light travelling in glass $(μ = 3 / 2)$ is incident on a horizontal glass air surface at the critical angle $θ_{C}$ . If a thin layer of water $(μ = 4 / 3)$ is now poured on the glass air surface, the ray of light emerge into air at the water air surface at an angle of $π / k$ radian. Find the value of $k$ .

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answer is 2.

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Detailed Solution

At point $O$

$μ_{1} \sin i = μ_{2} \sin r$

$\frac{3}{2} \sin θ_{c} = \frac{4}{3} \sin r, \frac{3}{2} \times \frac{2}{3} = \frac{4}{3} \sin r, \sin r = \frac{3}{4}$

At point E,

$\frac{4}{3} \times \sin r = 1 \times \sin θ$

$\Rightarrow \frac{4}{3} \times \frac{3}{4} = 1 \times \sin θ$

$\sin θ = 1, θ = \frac{π}{2}$

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