Question

A cube of side 2 m is placed in front of a concave mirror focal length 1m with its face P at a distance of 3 m and face Q at a distance of 5 m from the mirror. The distance between the images of face P and Q and height of images of P and Q are

• A. 1 m, 0.5 m, 0.25 m
• B. 0.5 m, 1 m, 0.25 m
• C. 0.5 m, 0.25 m, 1m
• D. 0.25 m, 1m, 0.5 m

Answer 1

The correct option is D 0.25 m, 1m, 0.5 m

For surface P,$\frac{1}{v_1}=\frac{1}{f}-\frac{1}{u}=1-\frac{1}{3}=\frac{2}{3}\Rightarrow v_1=\frac{3}{2}m$
For surface Q,$\frac{1}{v_2}=\frac{1}{f}-\frac{1}{u}=1-\frac{1}{5}=\frac{4}{5}\Rightarrow v_2=\frac{5}{4}m$
$\therefore v_1-v_2$ = 0.25 cm

Magnification of $P=\frac{v_1}{u}=\frac{3/2}{3}=\frac{1}{2}$

$\therefore$ Height of $P=\frac{1}{2}\times 2=1m$

Magnification of $Q=\frac{v_2}{u}=\frac{\frac{5}{4}}{5}=\frac{1}{4}$

$\therefore$ Height of $Q=\frac{1}{4}\times 2=0.5m$