Question

Two thin similar convex glass pieces are joined together front to front, with its rear portion silvered such that a sharp image is formed 0.2 m for an object at infinity. When the air between the glass pieces is replaced by water $⟮\mu =\frac{4}{3}⟯$, find the position of image.

Answer 1

On introducing air between the glasses system will act the convex mirror.

$\frac{1}{v}$=$\frac{1}{u}$+$\frac{2}{R}$

$\frac{2}{20}$=$\frac{2}{R}$

R=20cm.

When the space between the two peices will filled with the water then it will be a convex lens of water polished at one surface.This will act as convex mirror of focal length given by,

$\frac{1}{f}$=$2\times \frac{(2\mu -1)}{R}$

=$\frac{(4\mu -2)}{R}$=$(4\times \frac{4}{3}-2)/20$=$\frac{1}{6}$

$\frac{2}{u}$=$\frac{1}{6}$

u=12cm