A screen is placed 80 cm from an object. The image of the object on the screen is formed by a convex lens placed between them at two different locations separated by a distance 20 cm. The focal length of the lens is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 18.75 cm
In the displacement method, with object and screen a fixed distance D apart, a convex lens forms a sharp image at two positions separated by x. The two positions are interchangeable: the object distance at one is the image distance at the other.
\( \displaystyle u + v = D \qquad v - u = x \)
\( \displaystyle u = \frac{D - x}{2} \qquad v = \frac{D + x}{2} \)
Putting these into the lens formula \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \) (magnitudes, real image):
\( \displaystyle f = \frac{uv}{u + v} = \frac{D^{2} - x^{2}}{4D} \)
\( \displaystyle f = \frac{(80\,\mathrm{cm})^{2} - (20\,\mathrm{cm})^{2}}{4 \times 80\,\mathrm{cm}} \)
\( \displaystyle f = \frac{6400 - 400}{320}\,\mathrm{cm} = 18.75\,\mathrm{cm} \)
Note: NTA picked this question from an NCERT (2026-27) exercise and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Exercises – …
