$A$ plane mirror is placed $22.5\; cm$ in front of a concave mirror of focal length $10\; cm$. An object is placed between the two mirrors such that the images formed by both mirrors coincide. Find the magnification of the image produced by the concave mirror.

An electric lamp is fixed at the ceiling of a circular tunnel as shown in the figure. What is the ratio of the intensities of light at base $A$ and a point $B$ on the wall?

Discuss the sign convention of distances for reflection by a spherical mirror and refraction by a spherical lens.

$A$ camera objective has an aperture diameter $d.$ If the aperture is reduced to diameter $d/2,$ the exposure time under identical conditions of light should be made

The flat bottom of a cylindrical tank is silvered and water $(\mu = 4/3)$ is filled in the tank up to a height $h$. $A$ small bird is hovering at a height $3h$ from the bottom of the tank. When a small hole is opened near the bottom of the tank,the water level falls at the rate of $1\, cm/s$. The bird will perceive that its image's velocity is:

$A$ $2\,m$ long scale with a least count of $0.2\,cm$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $80\,cm$ mark and $1\,m$ mark, respectively. The image of the object pin on the other side of the lens coincides with the image pin that is kept at $180\,cm$ mark. The $\%$ error in the estimation of focal length is