Two thin convex lenses, when in contact, produce a combination of power + 10 D. When they are 0.25 m apart, the power reduces to + 6 D. The ratio of their focal lengths is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.25
For two thin lenses in contact the powers simply add. When they are separated by a distance d, the combined power is \( P = P_1 + P_2 - dP_1P_2 \), with d in metres.
\( \displaystyle P_1 + P_2 = 10\,\mathrm{D} \)
\( \displaystyle P_1 + P_2 - dP_1P_2 = 6\,\mathrm{D} \)
\( \displaystyle 10 - 0.25\,P_1P_2 = 6 \Rightarrow P_1P_2 = 16 \)
So \( P_1 \) and \( P_2 \) are the roots of \( x^{2} - 10x + 16 = 0 \):
\( \displaystyle (x - 2)(x - 8) = 0 \Rightarrow P_1 = 2\,\mathrm{D},\; P_2 = 8\,\mathrm{D} \)
\( \displaystyle f_1 = \frac{1}{2}\,\mathrm{m} = 0.5\,\mathrm{m} \qquad f_2 = \frac{1}{8}\,\mathrm{m} = 0.125\,\mathrm{m} \)
\( \displaystyle \frac{f_2}{f_1} = \frac{0.125\,\mathrm{m}}{0.5\,\mathrm{m}} = 0.25 \)
Taken the other way round the ratio is 4, which is not among the options.
Note: This question is from beyond the NCERT textbook and it appears to be out of the CUET 2026 Physics syllabus.