Two thin lenses of focal lengths f_1 and f_2 are in contact and coaxi…

The correct answer is Option (4) → \( \displaystyle\frac{f_1+f_2}{f_1 f_2} \)

For thin lenses in contact the powers add, because the focal lengths combine as \( \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \), and the power of a lens is \( P = 1/f \).

    \( \displaystyle P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2} = \frac{f_1 + f_2}{f_1 f_2} \)

Note: A similar question was also asked in CUET (UG) 2026 on 19-05-2026 (Slot 1), and in CUET (UG) 2023 on 12-06-2023 (Slot 3).

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):
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

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

In terms of power, Eq. (9.31) can be written as

    \( \displaystyle P = P_1 + P_2 + P_3 + \ldots \qquad (9.32) \)

where P is the net power of the lens combination.”