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About the years 214-212 BC, the Greek philosopher and scientist Archimedes is said to have repelled a Roman attack with a "death-ray" concave 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 500 meters away, what would need to be the radius of curvature of the mirror in order to achieve maximum effect?

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