A thin lens \( L_1 \) of focal length 20 cm placed in combination with another thin lens \( L_2 \) acts as a lens of focal length 12.5 cm. The power of \( L_2 \) is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3 D
For thin lenses in contact the powers add, \( P = P_1 + P_2 \), with each power \( P = 1/f \) and \( f \) in metres.
\( f_1 = 20\,\mathrm{cm} = 0.20\,\mathrm{m} \)
\( f = 12.5\,\mathrm{cm} = 0.125\,\mathrm{m} \)
\( \displaystyle P_1 = \frac{1}{0.20\,\mathrm{m}} = 5\,\mathrm{D} \qquad P = \frac{1}{0.125\,\mathrm{m}} = 8\,\mathrm{D} \)
\( P_2 = P - P_1 = 8\,\mathrm{D} - 5\,\mathrm{D} = 3\,\mathrm{D} \)