A screen is placed 90cm from an object. The image of the object on the screen formed by a convex lens at two different locations separated by 20 cm. The focal length of the lens is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 21.4 cm
This is the displacement method. For a fixed object-screen distance \( D \), a convex lens forms a sharp image at two positions, separated by \( d \); in the two positions the object and image distances are simply interchanged.
\( u + v = D = 90\,\mathrm{cm} \)
\( v - u = d = 20\,\mathrm{cm} \quad (\text{magnitudes}) \)
\( u = 35\,\mathrm{cm} \)
\( v = 55\,\mathrm{cm} \)
From the lens formula for a real image, with these magnitudes,
\( \displaystyle f = \frac{uv}{u + v} = \frac{D^{2} - d^{2}}{4D} \)
\( \displaystyle f = \frac{(90)^{2} - (20)^{2}}{4 \times 90} = \frac{8100 - 400}{360}\,\mathrm{cm} \)
\( \displaystyle f = \frac{7700}{360}\,\mathrm{cm} \approx 21.4\,\mathrm{cm} \)
Shortcut: Use \( f = (D^{2} - d^{2})/(4D) \) directly: \( 7700/360 \approx 21.4\,\mathrm{cm} \).
Note: A similar question was also asked in CUET (UG) 2025 on 13-05-2025 (Slot 1).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
