The sun (diameter $D$) subtends an angle $\theta$ at the pole of a concave mirror of focal length $f$. What will be the diameter of the image formed by the mirror?

You are asked to design a shaving mirror assuming that a person keeps it $10\,cm$ from his face and views the magnified image of the face at the closest comfortable distance of $25\,cm$. The radius of curvature of the mirror would then be.....$cm$.

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 . . . . . $\text{cm s}^{-1}$.

What is linear magnification? Obtain the equation of linear magnification for a concave mirror.

The circular boundary of the concave mirror subtends a cone of half-angle $\theta$ at its centre of curvature. The minimum value of $\theta$ for which a ray incident on this mirror parallel to the principal axis suffers more than one reflection is......$^o$

An object is placed in front of a concave mirror of focal length $15 \ cm$. The image formed is twice the size of the object. If the image is virtual,the position of the object is at ...... $cm$.