What is the relation between radius of curvature and focal length of a spherical mirror?

The radius of curvature of a converging mirror is $30 \mathrm{cm}$. At what distance from the mirror should an object be placed so as to obtain a virtual image?

Which of the following statements is not true in reference to the diagram shown above?

A student holding a mirror in his hand, directed the reflecting surface of the mirror towards the Sun. He then directed the reflected light on to a sheet of paper held close to the mirror.

Which type of mirror does he have?

An object of height $4 \mathrm{cm}$ is kept at a distance of $30 \mathrm{cm}$ from the pole of a diverging mirror. If the focal length of the mirror is $10 \mathrm{cm}$, the height of the image formed is ____.

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_1$ from $C$ and the distance of the image formed is $d_2$ from $C,$ the radius of curvature of this mirror is:

In which of the following is a concave mirror is used?

What should he do to burn the paper?

A point object is moving uniformly towards the pole of a concave mirror of focal length $25 \mathrm{cm}$ along its axis as shown below. The speed of the object is $1 {\mathrm{ms}}^{-1}$. At $t=0$, the distance of the object from the mirror is $50 \mathrm{cm}$. The average velocity of the image formed by the mirror between time $t=0$ and $t=0.25 \mathrm{s}$ is:

An object is placed at a distance of $12 \mathrm{cm}$ from a convex lens. A convex mirror of focal length $15 \mathrm{cm}$ is placed on another side of the lens at $8 \mathrm{cm}$ as shown in the figure. The image of the object coincides with the object.

When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be $\_\_\_ \mathrm{cm}$

Establish the relation between the radius of curvature $R$ and focal length $f$ of the spherical concave mirror.

For the diagram shown, according to the new Cartesian sign convention the magnification of the image formed will have the following specifications.

A student holding a mirror in his hand, directed the reflecting surface of the mirror towards the Sun. He then directed the reflected light on to a sheet of paper held close to the mirror.

Will he be able to determine the approximate value of focal length of this mirror from this activity ? Give reason and draw ray diagram to justify your answer in this case.