Question

A diverging lens of focal length 20 cm and a converging lens of focal length 30 cm are placed 15 cm apart with their principal axes coinciding. Where should an object be placed on the principal axis so that its image is formed at infinity ?

Answer 1

Given that :

$f_1=$ focal length of converging lens

= 30 cm

$f_2=$ focal length of diverging lens.

= 20 cm

and d = distance between them = 15 cm

Let, F = equivalent focal length

So, $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$

$=\frac{1}{30}+\left(\frac{1}{20}\right)-\left(\frac{5}{30(-20)}\right)$

$=\frac{1}{1.20}$

$\Rightarrow F=120\text{cm}$

$\Rightarrow$ The equivalent lens is a converging one. Distance from diverging lens so that emergent beam is parallel (image at infinity)

$d_1=\frac{dF}{f_1}=\frac{15\times 120}{30}=60\text{cm}$

It should be placed 60 cm left to diverging lens. Object should be placed,

(120 - 60) = 60 cm from diverging length.

Similarly, $d_2=\frac{dF}{f_2}=\frac{15\times 120}{20}$

= 90 cm

So, it should be placed (120 + 90)l cm

= 210 cm right to converging lens.