The refractive index of the material of a prism is 2 and its...

The refractive index of the material of a prism is

\sqrt{2}

and its refracting angle is

30^{\circ}

. One of the refracting surface of the prism is made a mirror inward. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is: $The refractive index of the material of a prism is 2 and its refracting angle is 30^ . One of the refracting surface of$ $The refractive index of the material of a prism is 2 and its refracting angle is 30^ . One of the refracting surface of$

Options

A $45^{\circ}$
B $60^{\circ}$
C0
D $30^{\circ}$

Correct answer

A. $45^{\circ}$

Step-by-step solution

Here

\angle r=30^{{}^{\circ}}

$The refractive index of the material of a prism is 2 and its refracting angle is 30^ . One of the refracting surface of$
(Using law of triangle)

\begin{aligned}& \Rightarrow \quad \mu=\frac{\sin i}{\sin r}\\ & \Rightarrow \sqrt{2} \cdot \sin30^{{}^{\circ}}=\sin i \\ & \Rightarrow \quad \sin i=\frac{1}{\sqrt{2}}\\ & \Rightarrow \quad i=45^{{}^{\circ}} \end{aligned}

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