Light is incident from glass $\left(\mathrm{\mu }=\frac{3}{2}\right)$ side on interface of glass and air. Find the angle of incidence for which the angle of deviation is $90°$.

At what values of the refractive index of a rectangular prism can a ray travel as shown in the figure. The section of the prism is an isosceles triangle and the ray is normally incident onto the face $AC$.

Find the angle of deviation suffered by the light ray shown in figure for following two conditions The refractive index for the prism material is $\mu =3/2$.

(i) When the prism is placed in air $(\mathrm{\mu }=1)$

(ii) When the prism is placed in water $(\mathrm{\mu }=4/3)$

An object is placed $10 \mathrm{cm}$ away from a glass piece $(n=1.5)$ of length $20 \mathrm{cm}$ bounded by spherical surfaces of radii of curvature $10 \mathrm{cm}$. Find the position of final image formed after two refractions at the spherical surfaces.

There is a small air bubble inside a glass sphere $(\mu =1.5)$of radius 5 cm. The bubble is at $O$ at $7.5 \mathrm{cm}$ below the surface of the glass. The sphere is placed inside water $(\mu =\frac{4 }{3})$such that the top surface of glass is $10 \mathrm{cm}$ below the surface of water. The bubble is viewed normally from air. Find the apparent depth of the bubble.

A small object $Q$ of length $1 \mathrm{mm}$lies along the principal axis of a spherical glass of radius $R=10 \mathrm{cm}$ and refractive index is $3/2$. The object is seen from air along the principal axis from left. The distance of object from the centre$P$ is $5 \mathrm{cm}$. Find the size of the image. Is it real, inverted?