Question

An object is placed at a distance of 12 cm from the optical centre of a convex lens of focal length 20 cm, as shown:


Answer the following questions based on the given details.

ii. If instead of this lens, we use a lens whose focal length is 0.75 times the given focal length, what effect will there be on the power of the lens?

[1 mark]

• A. Power of the lens would decrease by 2 times.
• B. Power of the lens would become half.
• C. Power will not change.
• D. Power of the lens would increase by 1.3 times.

Answer 1

The correct option is D Power of the lens would increase by 1.3 times.

Power of a lens is the reciprocal of focal length.
Given,
Initial focal length,
$f_1$= 20 cm = 0.2 m
Focal length of the new lens,
$f_2$ = 0.75 × 20 cm = 15 cm = 0.15 m

Let the initial power be $P_1$ and the new power be $P_2$.

$P_1=\frac{1}{f_1}=\frac{1}{0.20}=5D$

$P_2=\frac{1}{f_2}=\frac{1}{0.15}=6.66D$

$\frac{P_2}{P_1}=\frac{6.66}{5}=1.33$

Hence, the power increases by 1.33 times if the focal length of the new lens is 0.75 times the given focal length.