Question:
What is the focal length (f) of a combination of lenses (convex and concave) as given below? $f_{1}=30$, $f_{2}=20$
What is the focal length (f) of a combination of lenses (convex and concave) as given below? $f_{1}=30$, $f_{2}=20$
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Convex = (+), Concave = (-). Always use sign conventions when adding lens powers!
Updated On: May 13, 2026
- 30 cm
- 20 cm
- 10 cm
- 60 cm
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The Correct Option is D
Solution and Explanation
Step 1: Concept
The power of a lens combination is the sum of individual powers: $P = P_1 + P_2$, which implies $1/f = 1/f_1 + 1/f_2$.
Step 2: Meaning
For a convex lens, focal length is positive ($f_1 = +30$ cm). For a concave lens, focal length is negative ($f_2 = -20$ cm).
Step 3: Analysis
Calculate the effective focal length: $1/f = 1/30 + 1/(-20) = 1/30 - 1/20 = (2 - 3)/60 = -1/60$. This gives $f = -60$ cm.
Step 4: Conclusion
The magnitude of the focal length for the combination is 60 cm. Final Answer: (D)
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