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 total 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 ${178}^{\circ }$

${\delta }_{prim}=(\mu -1)A=(1.5-1)4{}^{\circ }=2{}^{\circ }$

${\delta }_{total}={\delta }_{prism}+{\delta }_{mirror}$

$=(1.5-1)4{}^{\circ }+(180-2\times 2{}^{\circ })$

$=2{}^{\circ }+176{}^{\circ }=178{}^{\circ }$

The ray diagram is shown in figure.
Hence, the correct answer is option (c).

Why this question? Note: The deviation caused by the combination of prism and mirror is the sum of deviation caused by prism and mirror individually, since both are in clockwise sense.