Write the mirror equation for a spherical mirror.

$A$ point object is placed at a distance of $10 \ cm$ and its real image is formed at a distance of $20 \ cm$ from a concave mirror. If the object is moved by $0.1 \ cm$ towards the mirror,the image will shift by about:

An object of height $5 \, cm$ is placed at a distance of $1 \, m$ from a concave mirror of radius of curvature $20 \, cm$. What will be the height of the image in $cm$?

Draw the ray diagram when an object is placed between the focus $(F)$ and the pole $(P)$ of a concave mirror.

An object and a concave mirror of focal length $f=10 \text{ cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_0=15 \text{ cm s}^{-1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$. When $u=30 \text{ cm}$,the speed of the mirror $V_m$ is such that the image is instantaneously at rest with respect to the laboratory frame,and the object forms a real image. The magnitude of $V_m$ is . . . . . $\text{cm s}^{-1}$.

The cross-section of a reflecting surface is represented by the equation $x^{2}+y^{2}=R^{2}$ as shown in the figure. $A$ ray travelling in the positive $x$ direction is directed toward the positive $y$ direction after reflection from the surface at point $M$. The coordinate of the point $M$ on the reflecting surface is