Question

Two lenses of focal lengths $20cm$ and $-40cm$ are held in contact. The image of an object at infinity will be formed by the combination at

• A. $10cm$
• B. $20cm$
• C. $40cm$
• D. infinity

Answer 1

Answer: (C)

Equivalent focal length is given by,
$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$
Here, $f_1=20cm$ and $f_2=-40cm$
$\therefore \frac{1}{f}=\frac{1}{20}-\frac{1}{40}=\frac{2-1}{40}$
$\Rightarrow f=40cm$
$\because \frac{1}{f}=\frac{1}{v}-\frac{1}{u}=\frac{1}{v}=\frac{1}{v}-\frac{1}{\infty }$
$\Rightarrow v=f=40cm\left[\because u=\infty \right]$