An empty tank has concave murror as its bottom. When sunlight falls normally on the mirror, it is focussed $\mathrm{a}_2$ height of 32 cm from the mirror. If the tank is filled with water upto a height of 20 cm , then the sunlight focusses at (refractive index of water $=\frac{4}{3}$ )

A convex lens of focal length 25 cm and made of glass with refractive index 1.5 is immersed in water. the absolute change in focal length of the glass is [use refractive index of water $=4 / 3$ ]

What is the refractive index of the material of a double convex lens having radii of curvature of 5 cm and 10 cm and focal length of $\frac{20}{3} \mathrm{~cm}$

A spherical glass is attached to a rigid wall as shown in the figure. An observer located at point $O$ is looking at a point $A$ on the wall. The refractive index of the glass is 1.5 and that of air is 1.0 . The distances are $O A=8 \mathrm{~cm}$, $X A=3 \mathrm{~cm}$. If the radius of curvature of spherical glass surface is $R=5 \mathrm{~cm}$, then the apparent distance of $A$ from observer $O$ is