Calculate the lateral displacement of a ray light passing through a $15 \mathrm{cm}$ Thick slab of glass, the opposite sides of which are parallel to each other. The angle of incidence of the ray is $60°.$R.I. of glass $=1.5.$

A container contains water up to a height of $20 \mathrm{cm}$ and there is a point source at the centre of the bottom of the container. A rubber ring of radius $r$ floats centrally on the water. The ceiling of the room is $2.0 \mathrm{m}$ above the water surface.

(a) Find the radius of the shadow of the radius of the ring formed on the ceiling if $r=15 \mathrm{cm}$.

(b) Find the maximum value of $r$ for which the shadow of the ring is formed on the ceiling. Refractive index of water$=\frac{4}{3}$.

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i . The reflected and the refracted rays make an angle of $90°$ with each other. The angles of reflection and refraction are $i and r\text{'}$ Show that the critical angle ${\theta }_c$ is given by ${\theta }_c={\sin }^{-1}\left(\tan r\right)$