Question

A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis ?

Answer 1

If the image in the mirror will from at the focus of the converging lens, then after transmission through the lens the rays of light will go parallel.

Let the object is at a distance x cm from the mirror.

$u=-x\text{cm}$

$v=25-15=+10\text{cm}$

(.... focal length of lens = 25 cm)

f = +40 cm

$\Rightarrow \frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{x}=\frac{1}{10}-\frac{1}{40}$

$\Rightarrow x=\frac{40}{3}$

The object is at distance

$(15-\frac{40}{3})=\frac{5}{3}$

= 1.67 cm from the lens.