Question

A converging lens of focal length 30 cm and diverging lens of focal length 20 cm are kept 15 cm apart with their principal axes coinciding. Where shall an object be placed to form an image at infinity?

• A. 60 cm from converging lens
• B. 60 cm from diverging lens
• C. 210 cm from diverging lens
• D. 210 cm from converging lens

Answer 1

Answer: (B), (D)

The correct options are
B 60 cm from diverging lens
D 210 cm from converging lens

Two cases are possible.

case 1: final image is formed by the concave lens for concave lens $v=infinity$ ; $f=-20$

=> $v=+20$

now $v=20+15=35$ serves as image distance for the convex lens

$v=+35$ ; $f=+30$

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

$\frac{1}{35}-\frac{1}{u}=\frac{1}{30}$

$u=-210$

$210$ from converging lens

case 2: final image is formed by convex lens

$v=infinity$ ; $f=+30$

=> $u=-30$ for convex lens to form image at infinity

so for the concave lens the image distance is $v=-30-(-15)=-15$ ; $f=-20$

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

$\frac{1}{-15}-\frac{1}{u}=\frac{1}{-20}$

$u=-60$

i.e, $60cm$ from diverging lens . hence correct option are $B,D$.