Question:
The plano-convex lens of focal length \(20\ \text{cm}\) and \(30\ \text{cm}\) are placed together to form a double convex lens, the final focal length will be
The plano-convex lens of focal length \(20\ \text{cm}\) and \(30\ \text{cm}\) are placed together to form a double convex lens, the final focal length will be
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Power of lens \(P = \frac{1}{f}\) in diopters (metres). Total power = sum of individual powers.
Updated On: Apr 23, 2026
- \(12\ \text{cm}\)
- \(60\ \text{cm}\)
- \(20\ \text{cm}\)
- \(30\ \text{cm}\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
For lenses in contact, \(\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}\).
Step 2: Detailed Explanation:
Given \(f_1 = 20\ \text{cm}\), \(f_2 = 30\ \text{cm}\).
\(\frac{1}{F} = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12}\)
\(\Rightarrow F = 12\ \text{cm}\).
Step 3: Final Answer:
Thus, focal length = \(12\ \text{cm}\).
For lenses in contact, \(\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}\).
Step 2: Detailed Explanation:
Given \(f_1 = 20\ \text{cm}\), \(f_2 = 30\ \text{cm}\).
\(\frac{1}{F} = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12}\)
\(\Rightarrow F = 12\ \text{cm}\).
Step 3: Final Answer:
Thus, focal length = \(12\ \text{cm}\).
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