Question

For an equilateral prism, it is observed that when a ray strikes grazingly at one face it emerges grazingly at the other. Its refractive index will be

• A. $\sqrt{3}$
• B. $\frac{2}{\sqrt{3}}$
• C. $2$
• D. Data not sufficient

Answer 1

Answer: (C)

Step 1: Given that:

Prism is equilateral; that is

Prism angle(A) = ${60}^0$

Step 2: Calculation of angle of refraction:

As the ray of light strikes grazingly,

Angle of incidence($\angle i$) = ${90}^0$

Angle of emergence($\angle e$) = ${90}^0$

By Snell's law;

For incidence;

${\mu }_1\sin i={\mu }_2\sin r_1$

${\mu }_1\sin {90}^0={\mu }_2\sin r_1$

$\because {\mu }_1=\sin {90}^0=1$

${\mu }_2\sin r_1=1$ ..........(1)

And similarly for emergence;

${\mu }_2\sin r_2={\mu }_1\sin e$

${\mu }_2\sin r_2=1.\sin {90}^0$

${\mu }_2\sin r_2=1$............(2)

From equation (1) and (2), we get;

$r_1=r_2$

Now,

$r_1+r_2=A$

$2r_1={60}^0$

$r_1={30}^0$

Step 3: Calculation of refractive index:

From equation (1), we get

${\mu }_2\sin {30}^0=1$

${\mu }_2\times \frac{1}{2}=1$

${\mu }_2=2$

Thus the refractive index will be 2.

Hence,

Option A) 2 is the correct option.