Question

A ray of light is incident at ${60}^o$ on a prism of refracting angle ${30}^o$. The emerging ray is at an angle ${30}^o$ with the incident ray. The value of refractive index of the prism is?

• A. $\frac{\sqrt{3}}{4}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\sqrt{3}$
• D. $\frac{2}{\sqrt{3}}$

Answer 1

The correct option is C $\sqrt{3}$

angle of prism A is 30

angle of incidence is 60 degree

angle of deviation is 30 degree

$i_1+i_2=A+\delta$

the angle of emegrance

$i_2=A+\delta -i_1=30+30-60=0$

'the emergent ray

$r_1+r_2=A$

$i_2=0,r_2=0$

$r_1=A={30}^0$

using snells law

$n=\frac{sin{i}_1}{sin{r}_1}=\frac{sin60}{sin30}=1.732$

since emergent ray is normal

$\delta ={\delta }_m={30}^0$

$\frac{sin(30+30/2)}{sin30/2}=1.732$