Q.A thin prism of refracting angle $5^{\circ}$, made of glass of refractive index $1.52$, is used to produce a small angle of deviation. Calculate this angle of deviation.

A prism, bounded by two plane faces inclined at a refracting angle $A$, refracts a ray twice (bending it towards the base on entry, away from the base on exit), producing a net angle of deviation $\delta$ that falls to one single minimum value $D_m$ as the angle of incidence is varied, at which point the ray inside the prism travels parallel to the base. At minimum deviation, $n=\dfrac{\sin\left(\frac{A+D_m}2\right)}{\sin\left(\frac A2\right)}$ (simplifying to $D_m=(n-1)A$ for a thin prism), giving the standard laboratory method for measuring r …