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?

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 

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

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