I don’t think that’s right. You’re assuming the intensity of the beam is constant over its entire area, which isn’t true. With a 5.24km flat circular mirror*, someone at the center of the beam would see the entire Sun reflected in the mirror and thus get the full solar irradiance. Someone near the edge would see only a small sliver of Sun and get much less.
*Technically a circular mirror would require the Sun’s light to arrive perpendicular to the mirror surface and reflect directly back, which would mean the Sun is behind the Earth, but that’s beyond the scope of this hypothetical (and can be solved with a suitable ellipse).
I don’t think that’s right. You’re assuming the intensity of the beam is constant over its entire area, which isn’t true. With a 5.24km flat circular mirror*, someone at the center of the beam would see the entire Sun reflected in the mirror and thus get the full solar irradiance. Someone near the edge would see only a small sliver of Sun and get much less.
*Technically a circular mirror would require the Sun’s light to arrive perpendicular to the mirror surface and reflect directly back, which would mean the Sun is behind the Earth, but that’s beyond the scope of this hypothetical (and can be solved with a suitable ellipse).