Question

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

Answer 1

It is given that for the convex lens,

Case 1.

$u=-40cm$

$f=+15cm$

Using lens formula

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

$\frac{1}{v}-\frac{1}{40}=\frac{1}{15}$

$\frac{1}{v}=\frac{1}{15}-\frac{1}{40}$

$v=+24.3cm$

The image in formed in this case at a distance of $24.3cm$ in left of lens.

Case 2.

A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens i.e. the source is placed at the focus of mirror, then the rays after reflection becomes parallel for the lens such that

$u=\infty$

$f=15cm$

Now, using mirror’s formula

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{1}{\infty }=\frac{1}{15}$

$v=+15cm$

The image is formed at a distance of $15cm$ in left of mirror