As shown,a narrow beam of light is incident onto a semi-circular glass cylinder of radius $R.$ Light can exit the cylinder when the beam is at the centre. When the beam is moved parallel to a distance $d$ from the central line,no light can exit the cylinder from its lower surface. Find the refractive index of the glass.

Rays from a point source of light situated at height $h$ below the liquid surface having refractive index $\mu$,form a circular patch of light of radius $r$ on the surface. The area of the patch is

$A$ glass prism whose cross-section is an isosceles triangle stands with its (horizontal) base in water; the angles that its two equal sides make with the base are each $\theta$. An incident ray of light,above and parallel to the water surface,is totally internally reflected at the glass-water interface and subsequently re-emerges into the air. Take the refractive indices of glass and water to be $\frac{3}{2}$ and $\frac{4}{3}$,respectively. The maximum value of $\cos\theta$ is:

When a ray of light emerges from a block of glass,the critical angle is

In the given figure,at the water-air interface,a light ray is incident at the critical angle. Find the value of $\mu_g$.

The relation between the critical angles of water and glass is: