A rod of length $5 \mathrm{cm}$ lies along the principal axis of a concave mirror of focal length $10 \mathrm{cm}$ in such a way that the end farther from the pole is $15 \mathrm{cm}$ away from it. Find the length of the image.

Two spherical mirrors (convex and concave) having the same focal length of $36 \mathrm{cm}$ are arranged as shown in the figure so that their optical axes coincide. The separation between the mirrors is $1 \mathrm{m}$. At what distance from the concave mirror should an object be placed so that its images formed by the concave and convex mirrors independently are identical in size?

A light ray falling at an angle of $45°$ with the normal on the surface of a clean slab of ice of thickness $1.00 \mathrm{m}$ is refracted into it at an angle of $30°$. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum$=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$.

In the given figure, an observer in air $(n=1)$ sees the bottom of a beaker filled with water $(n=4/3)$ upto a height of $40 \mathrm{cm}$. What will be the depth felt by this observer.

In the given figure, rays incident on an interface would converge $10 \mathrm{cm}$ below the interface if they continued to move in straight lines without bending. But due to refraction, the rays will bend and meet some where else. Find the distance of meeting point of refracted rays below the interface, assuming that the rays to be making small angles with the normal to the interface.