Question

A ray of light is incident on a prism as shown in the figure. The total deviation suffered by the ray is $\frac{x ^\circ }{2}$ . Then find $x$ . ( $\angle BAC=1^\circ $ and $\angle CAD=2^\circ $ , refractive indices are shown in figure.

Answer 1

We know that from Snell's law,
$n=\frac{sin \left(\frac{A + \delta}{2}\right)}{sin \left(\frac{A}{2}\right)}$
for small angles,
$n=\frac{\left(\frac{A + \delta}{2}\right)}{\left(\frac{A}{2}\right)}\Rightarrow nA=A+\delta\Rightarrow \delta=A\left(n - 1\right)$
where, $\delta,A\&n$ are the angle of deviation, the angle of the prism and refractive index of the prism,
$\Rightarrow \delta=\left(1 . 5 - 1\right)1+\left(2 - 1\right)2$
$=0.5+2=2.5$