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A lens having focal length f and aperture of diameter d forms an image of intensity I. Aperture of diameter d / 2 in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively:

1. f and I / 4
2. 3f / 4 and I / 2
3. f and 3I / 4
4. f / 2 and I / 2

Correct answer: f and 3I / 4

Solution

Covering half the aperture reduces the area of the lens by half, which reduces the light intensity to 3/4 of the original. The focal length remains unchanged as it depends only on the lens geometry and material, not the aperture size.

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