If two thin convex lenses are kept in contact, the focal length of th…

The correct answer is Option (2) → smaller than either focal length

For two thin lenses in contact the powers add, which in terms of focal lengths gives

    \( \displaystyle \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \)

Both lenses are convex, so \( f_1 \) and \( f_2 \) are positive. The sum of two positive terms is larger than either term, so \( \frac{1}{F} \gt \frac{1}{f_1} \) and \( \frac{1}{F} \gt \frac{1}{f_2} \), that is \( F \lt f_1 \) and \( F \lt f_2 \). For example, lenses of 20 cm and 30 cm in contact give \( \frac{1}{F} = \frac{1}{20}+\frac{1}{30} = \frac{1}{12} \), so \( F = 12\,\mathrm{cm} \).

NCERT (2026-27):
Combination of Thin Lenses in Contact – “… If several thin lenses of focal length f₁, f₂, f₃,... are in contact, the effective focal length of their combination is given by

    \( \displaystyle \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \dots \qquad (9.31) \)”