Question

For an object placed at a distance $20cm$ in front of a convex lens, the image is at a distance $20cm$ behind the lens. The focal length of convex lens is:

• A. $20cm$
• B. $10cm$
• C. $15cm$
• D. $40cm$

Answer 1

Answer: (B)

$10cm$

Answer is B.

There is a geometrical relationship between the focal length of a lens $f$, the distance from the lens to the bright object $o$ and the distance from the lens to the projected image $i$. The relationship between the distances is given as $\frac{1}{i}-\frac{1}{o}=\frac{1}{f}$.
It is given that object distance is -$20$ cm and the image distance is $20cm$. So, the focal length is given as $\frac{1}{20}+\frac{1}{20}=\frac{1}{0.1}$. The focal length $f=\frac{1}{0.1}=10cm.$

The focal length of the lens is 10 cm.