A point object is placed on the principal axis of a convex lens $(f=15 \mathrm{cm})$ at a distance of $30 \mathrm{cm}$ from it. A glass plate $(\mathrm{\mu }=1.50)$ of thickness $1 \mathrm{cm}$ is placed on the other side of the lens perpendicular to the axis. Locate the image of the point object.

Two convex lenses, each of focal length $10 \mathrm{cm}$, are placed at a separation of $15 \mathrm{cm}$ with their principal axes coinciding.

(a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system.

(b) Find the location of the virtual image formed by the lens system of an object placed far away.

(c) Find the focal length of the equivalent lens. (Note that the sign of the focal length is positive, although the lens system actually diverges a parallel beam incident on it).

A small block of mass $m$ and a concave mirror of radius $R$ fitted with a stand lies on a smooth horizontal table with a separation $d$ between them. The mirror together with its stand has a mass $m$. The block is pushed at $t=0$ towards the mirror so that it starts moving towards the mirror at a constant speed $V$ and collides with it. The collision is perfectly elastic. Find the velocity of the image

(a) at a time $t<\frac{d }{V}$,
(b) at a time $t>\frac{d}{V}$.