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# A prism of refractive index $\mu =1.5$ of vertical angle $6 ^{\circ}$ is placed in front of a mirror. A ray of light is incident normally on one of the face of the prism as shown. What is the total deviation caused by the system.

$(a)\;4^{\circ} \\ (b)\;3^{\circ} \\ (c)\;177^{\circ} \\ (d)\;174^{\circ}$

Total deviation caused
$\delta$ = deviation due to prism + deviation due to mirror.
$\delta = \delta_{ \large prism}+\delta_{\large mirror}$
$\qquad=( \mu-1 )A +180 -2 i$
$\delta _{\large prism }= (1.5 -1) 6^{\circ} =3 ^{\circ}$
angle of incidence for mirror $= 3^{\circ}$
$\therefore \delta _{\large mirror} = (180 - 2\times 3)$
$\qquad= 174$
$\delta _{\large total} = 3^{\circ} +174 ^{\circ}$
$\qquad= 177^{\circ}$
Hence c is the correct answer.

edited Jul 17, 2014