Two thin lenses are placed in contact. A convex lens of power $+5.0\text{D}$ and a concave lens of power $-2.0\text{D}$ are used. Find the focal length of the combination in centimeters.

Step-by-step solution

1. When lenses are in contact, their powers add algebraically: $P_{\text{total}}=P_1+P_2$.
2. Given $P_1=+5.0\text{D}$ and $P_2=-2.0\text{D}$, compute $P_{\text{total}}=+5.0-2.0=+3.0\text{D}$.
3. Focal length $f$ (in metres) is the reciprocal of power: $f=\frac{1}{P_{\text{total}}}=\frac{1}{3.0}\text{m}=0.333\text{m}$.
4. Convert metres to centimetres: $0.333\text{m}=33.3\text{cm}$. Wait, sign error: power $+3.0\text{D}$ gives a converging combination, so $f=\frac{1}{3.0}\text{m}=0.333\text{m}=33.3\text{cm}$. However the question asks for focal length of combination, not of each lens. Re‑check: the convex lens power is $+5.0\text{D}$ (f = 20 cm) and concave lens power is $-2.0\text{D}$ (f = -50 cm). Adding powers gives $+3.0\text{D}$, so $f=\frac{1}{3.0}\text{m}=0.333\text{m}=33.3\text{cm}$.

Concept tested: Power of thin lenses in contact

Published 1 September 2026 · How this solution was prepared and checked

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