The Lighthouse Lens Mystery · AI Generator #GEN-981D5888

Physics · optics

Problem

A lighthouse keeper notices that when sunlight passes through the lighthouse's large Fresnel lens (focal length f=2.0  mf = 2.0\;\text{m}), it creates a bright spot on the lighthouse wall. On a particular day, the sun appears to be at an infinite distance, and the lens creates a circular bright spot of diameter d=8.0  cmd = 8.0\;\text{cm} on the wall located L=2.4  mL = 2.4\;\text{m} from the lens. The keeper realizes this spot is actually the image of the sun itself! Given that the sun's actual diameter is D=1.39×109  mD = 1.39 \times 10^9\;\text{m} and the sun-Earth distance is R=1.50×1011  mR = 1.50 \times 10^{11}\;\text{m}, verify this claim by calculating what the diameter of the sun's image should be when formed by this lens.

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