Two thin lenses of focal lengths \( +10\,\mathrm{cm} \) and \( -5\,\mathrm{cm} \) are kept in contact. The power of combination is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -10\,\mathrm{D} \)
For thin lenses in contact, the powers add: \( P = P_1 + P_2 \), with \( P = 1/f \) and \( f \) in metres (power in dioptre).
\( f_1 = +10\,\mathrm{cm} = +0.1\,\mathrm{m} \)
\( f_2 = -5\,\mathrm{cm} = -0.05\,\mathrm{m} \)
\( \displaystyle P = \frac{1}{0.1\,\mathrm{m}} + \frac{1}{-0.05\,\mathrm{m}} = +10\,\mathrm{D} - 20\,\mathrm{D} = -10\,\mathrm{D} \)
The combination behaves as a diverging lens of focal length \( -10\,\mathrm{cm} \).