Which type of mirror can produce a virtual image?

$A$ ray of light enters from a medium with refractive index $n_1$ into a medium with refractive index $n_2$. If the angle of incidence is $\theta_1$ and the angle of refraction is $\theta_2$,then $\sin \theta_1 / \sin \theta_2 = \dots$

Discuss the position and nature of the image formed by a concave mirror when the object is moved from infinity towards the pole of the mirror.

The focal length of a concave mirror is $30 \, cm$. Find the position of the object in front of the mirror so that the image is three times the size of the object.

Where will the image of an object placed at the centre of curvature of a concave mirror form?

$A$ student focused the image of a candle flame on a white screen using a convex lens. He noted down the positions of the candle,screen,and lens as follows:
Position of candle $= 12.0 \, cm$
Position of convex lens $= 50.0 \, cm$
Position of the screen $= 88.0 \, cm$
$(i)$ What is the focal length of the convex lens?
$(ii)$ Where will the image be formed if he shifts the candle towards the lens to a position of $31.0 \, cm$?