A small black ball that absorbs all light rays, when illuminated by the Sun, heats up to temperature t1. To what temperature t2 will the ball heat up if the image of the Sun is focused on it using a lens with focal length F and diameter D? Assume that the energy lost by the ball per unit time due to heat exchange is proportional to its surface area and the temperature difference between the ball and the surrounding air. Take the air temperature equal to to. Consider the case when the diameter of the ball is smaller than the diameter of the image of the Sun. The angular diameter of the Sun is equal to a.

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