Appeared in: 2026 (3 sets)
(iii) If the distance between object and screen is $80.00\text{ cm}$ and the lens forms sharp images at two positions separated by $20.00\text{ cm}$., the focal length of convex lens is
(A) $15.50\text{ cm}$
(B) $18.75\text{ cm}$
(C) $20.50\text{ cm}$
(D) $22.75\text{ cm}$
✓ Verified CBSE Marking Scheme
Official Evaluation Steps & EL10 Insight
Correct Option: (B) 18.75 cm
Step 1 (Formula / Governing Law & Given Data): [1/4 Mark]
For the displacement method of a convex lens, the focal length $f$ is given by the formula:
$$f = \frac{D^2 - d^2}{4D}$$Where:
- $D = 80.00\text{ cm}$ (Distance between object and screen)
- $d = 20.00\text{ cm}$ (Distance between the two positions of the lens)
Step 2 (Step-by-Step Mathematical Working): [1/2 Mark]
Substituting the given values into the formula:
$$f = \frac{(80.00)^2 - (20.00)^2}{4 \times 80.00}$$ $$f = \frac{6400 - 400}{320}$$ $$f = \frac{6000}{320}$$ $$f = \frac{600}{32}$$ $$f = 18.75\text{ cm}$$Step 3 (Final Concluded Answer): [1/4 Mark]
The focal length of the convex lens is $18.75\text{ cm}$.
💡 EL10 Concept Insight:
Think of this like a seesaw: if you keep the object and screen fixed, there are two spots where the lens can "focus" the light—one where it's close to the object (making a big image) and one where it's far (making a small image). The math simply uses the gap between these two spots to calculate the lens's power.