A parallel beam of light is incident from air at an angle α on the side PQ of a right angled triangular…

A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right angled triangular prism of refractive index $n=\sqrt{2}$ . Light undergoes total internal reflection in the prism at the face PR when $\alpha$ has a minimum value of ${45}^o.$ The angle $\theta$ of the prism is:

1. ${15}^o$
2. ${22.5}^o$
3. ${30}^o$
4. ${45}^o$

Solution

$1\sin {45}^o=\sqrt{2}\sin r_1$
$r_2-r_1=\theta$
$\theta ={45}^o-{30}^o$
$\Rightarrow \theta ={15}^o$

Asked in: JEE Advanced 2016 (Paper 1)

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