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When the aperture is partially covered such that its diameter is halved, the focal length stays the same. However, the intensity decreases to one-fourth of its original value. What are the resulting focal length and intensity?

1. The focal length does not change, and the intensity becomes \( \frac{3I}{4} \).
2. The focal length doubles, and the intensity becomes \( \frac{I}{4} \).
3. The focal length does not change, and the intensity becomes \( \frac{I}{4} \).
4. The focal length doubles, and the intensity becomes \( \frac{3I}{4} \).

Correct answer: The focal length does not change, and the intensity becomes \( \frac{I}{4} \).

Solution

The focal length of a lens is a property of its curvature and refractive index, and it does not depend on the aperture size. When the aperture diameter is halved, the area of the aperture reduces to one-fourth, causing the intensity to also reduce to one-fourth. Hence, the focal length remains unchanged, and the intensity becomes I/4.

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