$A$ beam of light is converging towards a point $O$ behind a convex mirror of focal length $20 \, cm$. If the point $O$ is $10 \, cm$ behind the mirror,then the position of the image is at a distance of ..... $cm$.

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately $0.009$. The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature $0.4 \ m$ is

Write the mirror equation for a spherical mirror.

$A$ square of side $3 \ cm$ is placed at a distance of $25 \ cm$ from a concave mirror of focal length $10 \ cm$. The center of the square is on the axis of the mirror and the plane is perpendicular to the axis. The area enclosed by the image of the square is ........ $cm^2$.

$A$ virtual image three times the size of the object is obtained with a concave mirror of radius of curvature $36 \ cm$. The distance of the object from the mirror is ........ $cm$.

$A$ concave mirror forms a real image three times larger than the object on a screen. The object and screen are moved until the image becomes twice the size of the object. If the shift of the object is $6 \ cm$,find the shift of the screen and the focal length of the mirror.