A convex lens of focal length 5 cm is used as a simple microscope. The image is to be formed at the near point, 25 cm from the lens. The object should be placed in front of the lens at a distance of about
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4.2 cm
In a simple microscope the image is virtual and on the same side as the object. So, by the sign convention, \( v=-25 \) cm. The lens formula then gives \( u \).
\( v=-25\ \mathrm{cm} \)
\( f=+5\ \mathrm{cm} \)
\( \begin{aligned} \frac{1}{u} &= \frac{1}{v}-\frac{1}{f} \\ &= -\frac{1}{25}-\frac{1}{5} \\ &= -\frac{6}{25} \end{aligned} \)
\( u\approx-4.2\ \mathrm{cm} \)
Hence, the object should be about 4.2 cm in front of the lens, a little inside its focal length.
NCERT (2026-27):
The microscope – “… In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side. …”
Refraction by a lens – “… Applying the sign convention, BO = –u, DI = +v, we get”
\( \displaystyle \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \)\( \qquad (9.23) \)