From the mirror equation $\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{2}{\mathrm{R}},$ show that the image in a plane mirror is as far behind the mirror as the object is in front of it.

A convex lens forms a real and inverted image of a needle at a distance of $50 \mathrm{cm}$ from the lens. Where is the needle placed in front of the convex lens so that its image is of the same size as the object? Also find the power of the lens.

Show by a ray diagram the formation of an image by a convex mirror.

What is the minimum number of rays required for locating the image formed by a concave mirror for an object. Draw a ray diagram to show the formation of a virtual image by a concave mirror.

A convex lens has a focal length of $10 \mathrm{cm}$. At what distance from the lens should the object be placed so that it forms a real and inverted image $20 \mathrm{cm}$ away from the lens? What would be the size of the image formed if the object is $2 \mathrm{cm}$ high? With the help of a ray diagram show the formation of the image by the lens in this case.

The refractive indices of four media$\mathrm{A}, \mathrm{B}, \mathrm{C}$and $\mathrm{D}$ are given in the following table:

If light travels from one medium to another, in which case the change in speed will be (i) minimum, (ii) maximum.

At what distance should an object be placed from a lens of focal length $25 \mathrm{cm}$ to obtain its image on a screen placed on the other side at a distance of $50 \mathrm{cm}$ from the lens? What will be the magnification produced in this case?

What do you mean by optically denser and optically rarer media? How is the speed of light related to optical density?

With the help of neat ray diagrams show the path of reflected ray formed on reflection from a spherical mirror, when

(i) Incident ray passes through (or directed towards) the principal focus of mirror.