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A right angled prism is made up of a material of refractive index $μ$ . It is desired that a light ray incident normally on PQ emerges parallel to the incident direction after suffering two total internal reflection. In which of the following conditions is this possible ?

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Never possible

$μ = 1.3$

$μ = \sqrt{2}$

$μ = \sqrt{3}$

answer is A, B.

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Detailed Solution

As total internal reflection is taking place at both of the surfaces PR and RQ

$θ_{c} \leq θ and θ_{c} \leq 90^{0} - θ$

$\Rightarrow θ_{c} \leq 45^{0}$

${sinθ}_{c} \leq \frac{1}{\sqrt{2}} \Rightarrow \frac{1}{μ} \leq \frac{1}{\sqrt{2}}$

$\Rightarrow μ \geq \sqrt{2}$

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