An object is placed $50\, cm$ from a lens that produces a virtual image at a distance of $10\, cm$ in front of the lens. Calculate the focal length of the lens. (in $, cm$)

What is the nature of the image formed by an object placed at a distance of $10 \text{ cm}$ in front of a concave mirror with a focal length of $20 \text{ cm}$?

Give the relationship of magnification with focal length of a spherical mirror.

If the image formed by a convex lens is of the same size as that of the object,what is the position and nature of the image with respect to the lens?

How can you distinguish between a plane mirror,a convex mirror,and a concave mirror by merely looking at the image formed in each case?

The following table gives the values of refractive indices of a few media:

$S.No.$	$1$	$2$	$3$	$4$	$5$
Medium	Water	Crown glass	Rock salt	Ruby	Diamond
Refractive index	$1.33$	$1.52$	$1.54$	$1.71$	$2.42$

Use this table to give an example of $(i)$ a medium pair so that light speeds up when it goes from one of these media to another. $(ii)$ a medium pair so that light slows down when it goes from one of these media to another.