Question

A ray of light falls normally on one face of prism of refractive index $\sqrt{2}$ and comes out at grazing emergence from the second surface. The angle of prism is

• A. $30^{\circ }$
• B. $45^{\circ }$
• C. $60^{\circ }$
• D. $0^{\circ }$

Answer 1

Answer: (B)

Let angle of prism be $A$
As the ray of light falls normally on the first face of prism, therefore $i_1=0$
Applying Snell's law at the first face, we get
$1sin{i}_1=\mu sin{r}_1$
$\therefore r_1=0$

For a prism
$r_1+r_2=A$
$A=r_2$
Applying Snell's law at the second face, we get
$\mu sin{r}_2=1sine$
where $e$ is the angle of emergence
$\mu sin{r}_2=1sin90^{\circ }$ (From figure)
$sin{r}_2=\frac{1}{\mu }$
$r_2=si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)$
$r_2=45^{\circ }$
$\therefore A=45^{\circ }$ (From $\left(i\right))$