The refractive of the material of a prism of refracting angle $45°$ is 1.6 for a certain monochromatic ray. What should be the minimum angle of incidence of this ray on the prism so that no total internal reflection takes place as the ray comes out of the prism? 

Light enters a prism of angle A at a grazing incidence to emerge at angle $\theta$ with the normal. Show that the refractive index of the material of the prism is given by

$\mu ={\left[1+{\left(\frac{\cos A+\sin \theta }{\sin A}\right)}^2\right]}^{\frac{1}{2}}$

A right-angled prism is kept immersed in water. When a ray of light is allowed to be incident on one of the faces of the prism adjoining the right angle normal to the face, the ray is found to be totally reflected by the face opposite to the right angle and to emerge through the other face adjoining the right angle. But when the ray of light is allowed to be normally incident on the other face adjoining the right angle, it emerges through the face opposite to the right angle and there is total internal reflection.

If the other two angles of the prism be $60°$ and $30°$, what information can you gather about the refractive index of the material of the prism? Given RI of water with respect to vacuum$=1.33$ and $V_3=1.732.$

If a ray passes through the composite block without any deviation, show that ${\mu }_1{}^2+{\mu }_2^2+{\mu }_3{}^2=1.$