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

Answer: 49

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