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Q80
(NDA-I/2012)
Science & Technology › Basic Science (Physics, Chemistry, Biology) › Geometrical optics
Answer Verified
Two thin convex lenses of focal lengths 4 cm and 8 cm are separated by a distance of 4 cm in air. The combination will have the focal length
Result
Your answer:
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·
Correct:
A
Explanation
The correct answer is Option 1. When two thin lenses of focal lengths f₁ and f₂ are separated by a distance d, the effective focal length (F) of the combination is calculated using the formula:
1/F = 1/f₁ + 1/f₂ - d/(f₁f₂)
Given the values:
- f₁ = 4 cm
- f₂ = 8 cm
- d = 4 cm
Substituting these into the formula:
1/F = 1/4 + 1/8 - 4/(4 × 8)
1/F = 1/4 + 1/8 - 4/32
1/F = 1/4 + 1/8 - 1/8
The terms +1/8 and -1/8 cancel each other out, leaving 1/F = 1/4. Therefore, the effective focal length F = 4 cm. Options 2, 3, and 4 are incorrect as they do not account for the subtractive effect of the separation distance on the combined power of the lenses.
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