Question

A plot between the angle of deviation and angle of incidence for a prism is shown in the figure. From the graph one can say that the refracting angle of the prism is :

• A. ${47}^{\circ }$
• B. ${46}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${46}^{\circ }$

We know that the deviation produced by prism is given by :
$\delta =(i+e)-A$
where $e$ is angle of emergence.

$\Rightarrow$ From the given graph, $i$ and $e$ could be either ${38}^{\circ }$ or ${58}^{\circ }$ interchangeably and value of $\delta$ will be same for both cases.
So, ${50}^{\circ }={38}^{\circ }+{58}^{\circ }-A$
$(\because \delta ={50}^{\circ })$
$\Rightarrow A={96}^{\circ }-{50}^{\circ }={46}^{\circ }$

Why this question? Tip: Even if $i$ and $e$ are interchanged, we will get the same value of $\delta$ because of "reversibility principle of light".