Question

A certain prism is found to produce a minimum deviation of $38^{\circ}$. It produces a deviation of $44^{\circ}$ when the angle of incidence is either $42^{\circ}$ or $62^{\circ}$. What is the angle (in degree) of incidence when it is undergoing minimum deviation?

Answer 1

$\delta_{\min }=38^{\circ}$
$\delta_{\min }=2 i-A $
$38^{\circ}=2 i-A $....(i)
$\delta=i+r-A $
$44^{\circ}=42^{\circ}+62^{\circ}-A $
$A=60^{\circ}$ ....(ii)
From equations (i) and (ii),
$38^{\circ}=2 i-60^{\circ}$
$ \Rightarrow i=49^{\circ}$