FYKOS Year 29 Series 1 Problem 4 — the lethal lens · FYKOS 29 #29.1.4
Physics · mechanics · optics
Problem
Imagine that around the Sun on a circular orbit is a convex lens with a diameter that is equal to the diameter of the Sun, the focal point of which orbits with a sufficient precision on the orbit of Earth. Determine how the lens will burn the Earth during one of its orbit (ie. how much solar energy will be given to Earth by the lens), if it orbits at the distance of Mercury and compare it with the state where it will be as far as Venus.
Bonus: Consider the eclipse that the lens will cause during its orbit.