A convex lens of focal length \( 25 \) cm is placed coaxially in contact with a concave lens of focal length \( 20 \) cm. The power of the combination is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( -1\,\mathrm{D} \)
For thin lenses in contact the powers add: \( P = P_1 + P_2 \), with \( P = 1/f \) (\( f \) in metres) and the focal length of a concave lens negative.
\( f_1 = +25\,\mathrm{cm} = +0.25\,\mathrm{m} \Rightarrow P_1 = +4\,\mathrm{D} \)
\( f_2 = -20\,\mathrm{cm} = -0.20\,\mathrm{m} \Rightarrow P_2 = -5\,\mathrm{D} \)
\( P = +4 - 5 = -1\,\mathrm{D} \)
The combination behaves as a diverging lens of focal length \( -1\,\mathrm{m} \).