What is a lens?

$(a)$ What should be the position of the object,when a concave mirror is to be used $(i)$ as a shaving mirror,and $(ii)$ in torches producing a parallel beam of light? $(b)$ $A$ man standing in front of a mirror finds his image having a very small head and legs of normal size. What type of mirror is used in designing such a mirror?

When an object is placed at $2F$ in front of a convex lens,where will its image be formed?

$(a)$ State the relation between object distance,image distance and the focal length of a spherical mirror.
$(b)$ Draw a ray diagram to show the image formed by a concave mirror when an object is placed between the pole and focus of the mirror.
$(c)$ $A$ concave mirror of focal length $15\, cm$ forms an image of an object kept at a distance of $10\, cm$ from the mirror. Find the position,nature and size of the image formed by it.

The absolute refractive indices of glass and water are $4/3$ and $3/2$ respectively. If the speed of light in glass is $2 \times 10^{8} \ m \ s^{-1}$,calculate the speed of light in $(i)$ vacuum,$(ii)$ water.

State the sign convention used to measure distances from a mirror.