Question

A ray is passing through a broken prism as shown. Find the total deviation suffered by the light ray.

• A. ${105}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${15}^{\circ }$

Answer 1

The correct option is D ${15}^{\circ }$

The broken prism can be completed as shown in the figure.


From geometry,
$A+{60}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\Rightarrow A={180}^{\circ }°-{90}^{\circ }={90}^{\circ }$
Also, we know that the deviation produced by the prism is :
$\delta =(i+e)-A$
Here $i={45}^{\circ },e={60}^{\circ }$
$\Rightarrow \delta =({45}^{\circ }+{60}^{\circ })-{90}^{\circ }$
$\therefore \delta ={15}^{\circ }$

Why this question? Tip: Always complete the geometry of prism at first step to find prism angle $\left(A\right)$.