In about the years 214-212 BC, the Greek philosopher and scientist Archimedes is said to have repelled

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In about the years 214-212 BC, the Greek philosopher and scientist Archimedes is said to have repelled a Roman attack with a "death-ray" converging mirror, using sunlight to set the approaching fleet on fire. Assume an early morning attack from the east, with the Sun directly behind the ships. If the approaching fleet is \(100 \mathrm{~m}\) away from the mirror, what would the mirror's radius of curvature have to be in order to achieve the maximum effect? 

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