Question

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.

Answer 1

The object is placed in the focus of the converging mirror,

There will be two images

(a) One due to direct transmission of light through lens.

(b) One due to reflection and then transmission of the rays through lens.

Case-I: $\left(S^{{}^{\prime }}\right)$ For the image by direct transmission, u = -40 cm, f = 15 cm.

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

$\Rightarrow \frac{1}{v}=\frac{1}{15}+\frac{1}{(-40)}=\frac{40-15}{40\times 15}$

$\Rightarrow v=\frac{40\times 15}{40-15}$

= 24 cm (left of lens).

Case II: $\left(S^{{}^{\prime }}\right)$ Since the object is placed on the focus of mirror, after reflection the rays become parallel for the lens.

So, $u=0\Rightarrow f=15\text{cm}$

$\Rightarrow \frac{1}{v}-\frac{1}{u}=\frac{1}{15}$

$\Rightarrow v=15\text{cm}$ (left of lens)