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Q.

A ray of light falls normally an a refracting face of a prism $(μ = 1 .5)$ . Find the angle of the prism if the ray just fails to emerge from the prism.

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a

$\sin^{- 1} \frac{2}{3}$

b

$\sin^{- 1} \frac{1}{\sqrt{2}}$

c

$\sin^{- 1} \frac{3}{2}$

d

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

answer is B.

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Detailed Solution

From first face
$\begin{array}{l} i_{1} = 0, r_{1} = 0 \\ r_{1} + r_{2} = A \Rightarrow r_{2} = A \end{array}$
From second face
$r_{2} = θ_{c}$ ; i.e $r_{2} = θ_{c} = A$
As TIR is taking place
$\begin{array}{l} \sin θ_{c} = \frac{1}{μ} \\ \sin A = \frac{2}{3} \\ A = \sin^{- 1} (\frac{2}{3}) \end{array}$

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