Discussion Forum

1)

A parallel beam of light is incident from the air at an angle $\alpha$ 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 45⁰. The angle θ of the prism is

Answer:

Option A

Explanation:

Applying Snell's law at M,

$n=\frac{\sin \alpha}{\sin r_{1}}\Rightarrow\sqrt{2}=\frac{\sin 45^{0}}{\sin r_{1}}$

$\sin r_{1} = \frac{\sin 45^{0}}{\sqrt {2}}=\frac{1/ \sqrt{2}}{\sqrt{2}}=\frac{1}{2}$

$r_{1}=30^{0}$

$\sin \theta_{c} =\frac{1}{n}=\frac{1}{\sqrt{2}}\Rightarrow\theta_{c}=45^{0}$

Let us take r₂=θ_c=45⁰ for just satisfying the condition of TIR

In ΔPNM, θ+90+r₁+90-r₂=180⁰ or θ=15⁰