Question

A light source is placed $100cm$ away from a screen. A converging lens placed at a certain position between the source and the screen focuses the image of the source on the screen. The lens is moved a distance of $40cm$ and it is found that it again focuses the image of the source on the screen. The focal length of the lens is

• A. $21cm$
• B. $30cm$
• C. $40cm$
• D. $67cm$

Answer 1

Answer: (A)

$21cm$

Answer is A.
The expression for focal length by displacement method is given as follows.
$f=\frac{D^2-x^2}{4D}$
where,
D - the distance between the object and screen
x - the distance between the two positions of the lens.
Here, D = 100 cm and x = 40 cm.

So, $f=\frac{D^2-x^2}{4D}=\frac{{100}^2-{40}^2}{4\times 100}=21cm$.

Hence, the focal length of the lens is 21 cm.