Question

A 20 cm convex lens is placed in contact with a diverging lens of unknown focal length. The lens combination acts as a converging lens and has a focal length of 30 cm. What is the focal length of the diverging lens?​

Answer 1

Given:

A 20 cm convex lens is placed in contact with a diverging lens of unknown focal length. The lens combination acts as a converging lens and has a focal length of 30 cm.

To find:

Focal length of diverging lens ?

Calculation:

Let focal length of the diverging lens be f2 :

According to Combination of Lens:

$P_{net} = P1 + P2$

$\implies \: \dfrac{1}{f_{net}} = \dfrac{1}{f1} + \dfrac{1}{f2}$

$\implies \: \dfrac{1}{( + 30)} = \dfrac{1}{( + 20)} + \dfrac{1}{f2}$

$\implies \: \dfrac{1}{ 30} = \dfrac{1}{20} + \dfrac{1}{f2}$

$\implies \: \dfrac{1}{f2} = \dfrac{1}{30} - \dfrac{1}{20}$

$\implies \: \dfrac{1}{f2} = \dfrac{2 - 3}{60}$

$\implies \: \dfrac{1}{f2} = \dfrac{ - 1}{60}$

$\implies \: f2 = - 60 \: cm$

So, focal length of diverging lens is 60 cm.