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A ray of light falls from air on a prism of refractive index $μ = \sqrt{2}$ at an angle i with the normal. What should be the maximum value of i for which the total internal reflection will take place at side AC?

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45°

90°

30°

60°

answer is B.

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Detailed Solution

$r_{1} + r_{2} = 75^{\circ}; for total internal reflection r_{2} > i_{c}$

$\Rightarrow r_{2 (min)} = i_{c} = \sin^{- 1} (\frac{1}{\sqrt{2}}) = 45^{\circ}$

$\Rightarrow r_{1} (max) = 75^{o} - 45^{o} = 30^{\circ}$

$\sin (i) = μsin (r_{1 (max)})$

$\Rightarrow \sin (i) = \sqrt{2} \sin (30^{o}) \Rightarrow i = 45^{\circ}$

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