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

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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.

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