Question

A prism having an apex angle $4^{\circ }$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in figure. Through what angle is the ray deviated after reflection from the mirror?

• A. ${176}^{\circ }$
• B. $4^{\circ }$
• C. ${178}^{\circ }$
• D. $2^{\circ }$

Answer 1

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

${\delta }_{prism}=(\mu -1)A=(1.5-1)4^{\circ }=2^{\circ }$
$\text{Angle of incidence for plane mirror};i=2^{\circ }$

$\therefore {\delta }_{total}={\delta }_{prism}+{\delta }_{mirror}$
$=(\mu -1)A+({180}^{\circ }-2i)$
$=(1.5-1)4^{\circ }+({180}^{\circ }-2\times 2^{\circ })$
$=2^{\circ }+{176}^{\circ }={178}^{\circ }$