Question

P is a small angled prism of angle $3^o$ made of a material ($\mu =1.5$) . A ray of light is incident as shown in Fig. 13.80, M is a plane mirror. The angle of deviation for the ray reflected from the mirror M with respect to the incident ray is :

• A. ${4.5}^o$
• B. ${175.3}^o$
• C. ${177}^o$
• D. ${178.5}^o$

Answer 1

The correct option is D ${178.5}^o$

Given, $\mu =1.5$, $A=3^{\circ }$

For a small prism the angle of deviation is given by

${\delta }_P=\left(\mu -1\right)A$

$\Rightarrow {\delta }_P=\left(1.5-1\right)3=0.5\times 3={1.5}^{\circ }$

From figure, $i_m={1.5}^{\circ }$

For a mirror angle of deviation is given by

${\delta }_m=\pi -2i_m$

$\Rightarrow {\delta }_m=\pi -2\times 1.5={180}^{\circ }-3^{\circ }={177}^{\circ }$

The total deviation is given by

$\delta ={\delta }_P+{\delta }_m$

$\Rightarrow \delta =1.5+177={178.5}^{\circ }$

Hence the correct answer is option (D).