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
$1sini_{1}=\mu sinr_{1}$
$\therefore \, r_{1}=0$

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