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

Answer: 5

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,
$\Rightarrow \delta =\left(1.5-1\right)1+\left(2-1\right)2$
$=0.5+2=2.5$