Question

A convex lens produces clear images when placed at two positions between an object and a screen that are 1 m apart. If the distance between the two positions of the lens at which clear images are formed is 20 cm, the focal length of the lens is:

• A. 5 cm
• B. 24 cm
• C. 125 cm
• D. 12 cm

Hint:

Lens displacement method: $f = \dfrac{L^2 - d^2}{4L}$.
L = object-screen distance, d = distance between two lens positions for sharp images.
Check units: meters to cm conversion for answer options.

Answer 1

The Correct Option is D

• Let the object-screen distance $L = 1\ \text{m}$ and separation between lens positions $d = 0.2\ \text{m}$.
• For lens displacement method: $f = \dfrac{L^2 - d^2}{4L} = \dfrac{1^2 - 0.2^2}{4 \cdot 1} = \dfrac{1 - 0.04}{4} = 0.24\ \text{m} = 24\ \text{cm}$. Wait, the formula is correct: $f = \dfrac{L^2 - d^2}{4L} = 0.24\ \text{m}$, so correct answer is (2) 24 cm.
• Hence, focal length = 24 cm.