The power of a combination of convex lens of focal length 40 cm and a concave lens of focal length 25 cm when placed in contact is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -1.5 D
For thin lenses in contact, the powers add: \( P = P_1 + P_2 \), with \( P = 1/f \) and \( f \) in metres. By the sign convention, a convex lens has a positive focal length and a concave lens a negative one.
\( f_1 = +40\,\mathrm{cm} = +0.40\,\mathrm{m} \)
\( f_2 = -25\,\mathrm{cm} = -0.25\,\mathrm{m} \)
\( \displaystyle P_1 = \frac{1}{0.40} = +2.5\,\mathrm{D} \qquad P_2 = \frac{1}{-0.25} = -4\,\mathrm{D} \)
\( P = 2.5 - 4 = -1.5\,\mathrm{D} \)
The negative sign shows that the combination behaves as a diverging lens.