Refractive index of a prism is $\sqrt{7/3}$ and the angle of prism is $60^{\circ }$. The minimum angle of incidence of a ray that will be transmitted through the prism is

A ray is projected on face LM of the prism gets refracted from the two faces of the prism and finally emerges out of it.

For minimum $i$, the emergent ray must graze on the face LN i-e.  $e=90^o$

Using Snell's law for face LN,    $n_{2}sin{r}_2=n_{1}sine$

$\sqrt{\frac{7}{3}}sin{r}_2=1\times sin90^o$

This gives $r_2=40.89^o$

As $A=r_1+r_2$ ,$A=60^o$

$r_2=19.11^o$

Using snell's law for face LN,  $1\times sini=\sqrt{\frac{7}{3}}\times sin19.11^o$

This gives $i=30^o$