Question

Find the net angle of deviation produced by the system of a prism and a plane mirror as shown in the figure. The prism being very thin has a refracting angle of $4^{\circ }$ and the incident ray is parallel to the base of the prism as shown in the figure below.

• A. ${178}^{\circ }\text{anticlockwise}$
• B. ${80}^{\circ }\text{clockwise}$
• C. ${178}^{\circ }\text{clockwise}$
• D. ${180}^{\circ }\text{anticlockwise}$

Answer 1

The correct option is C ${178}^{\circ }\text{clockwise}$

Since the prism is thin, angle of deviation due to prism is,
${\delta }_1=A(\mu -1)$

Substituting the given data we get,

${\delta }_1=4^{\circ }(1.5-1)=2^{\circ }\text{clockwise}$

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

Angle of deviation due to plane mirror is,
${\delta }_2=({180}^{\circ }-2i)$

$\Rightarrow {\delta }_2=({180}^{\circ }-2\times 2^{\circ })={176}^{\circ }\text{clockwise}$

So, net deviation,

${\delta }_{net}={\delta }_1+{\delta }_2={178}^{\circ }\text{clockwise}$



Hence, option $\left(c\right)$ is the correct answer.

Why this Question? This question will help to understand how to approach a problem having deviation due to the combination of mirror and prism. Caution:- Direction of deviation is to be noted carefully.