Question

A prism having an apex angle of $4^0$ and refractive index of 1.50 is located in front of a vertical plane mirror as shown in the figure. A horizontal ray of light is incident on the prism. The total angle through which the ray is deviated is :

• A. $4^0$ clockwise
• B. ${178}^0$ clockwise
• C. $2^0$ clockwise
• D. $8^0$ clockwise

Answer 1

The correct option is B ${178}^0$ clockwise

Given: A prism having an apex angle of $4^{\circ }$ and refractive index of 1.50 is located in front of a vertical plane mirror as shown in the figure . A horizontal ray of light is incident on the prism .

To find the total angle through which the ray is deviated

Solution:

For small angle prism,

${\delta }_1=(\mu -1)A⟹{\delta }_1=(1.5-1)\left(4\right)⟹{\delta }_1=2^{\circ }$

So ray is incident on plane mirror at $2^{\circ }$,

Hence ${\delta }_2=S_{mirror}={180}^{\circ }-2\left(2^{\circ }\right)={176}^{\circ }$

Total reflection = ${\delta }_1+{\delta }_2={176}^{\circ }+2^{\circ }={178}^{\circ }$ clockwise.