Question:
A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in the central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:
A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d/2 in the central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:
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• Aperture affects intensity
• Focal length depends only on lens geometry
Updated On: Mar 19, 2026
- \(f,\; \dfrac{I}{4}\)
- \(\dfrac{3f}{4},\; I\)
- \(f,\; \dfrac{3I}{4}\)
- (f)/(2), (I)/(2)
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The Correct Option is C
Solution and Explanation
Step 1: Focal length of a thin lens depends only on refractive index and curvatures, not on aperture. ⟹ f remains unchanged
Step 2: Original aperture area: A=π((d)/(2))²=(π d²)/(4)
Step 3: Blocked central area: Ab=π((d)/(4))²=(π d²)/(16)
Step 4: Transmitting area: A'=(3π d²)/(16)
Step 5: Intensity ∝ aperture area: I'=(A')/(A)I=(3)/(4)I
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