You can’t get away with less because a mirror can’t appear brighter than what it’s reflecting; this is a fundamental property of optical systems.
I can understand that a single flat mirror cannot ever appear brighter than whatever is being reflected. But why can’t multiple mirrors pointed at one spot have a total intensity greater than that of any one of the mirrors (or a curved dish that focuses the light)?
Multiple mirrors reflecting sunlight can indeed result in an irradiance greater than that of the Sun (this is how solar power towers work). But to do that, you need to cover more than a 0.5° circle of the sky with mirrors. The total irradiance can be as high as you want (up to covering the whole sky with mirrors, which would be equivalent to standing on the surface of the Sun) but the irradiance per angular area can never be higher than the Sun’s.
You can think of it as dividing a mirror of any shape into a bunch of flat mirrors. Each mirror can only show you a reflection of part of the Sun (which is exactly as bright as that part of the Sun) but you can have as many mirrors as you want showing the same part of the Sun, multiplying the light you receive from it (up to filling the entire sky once again).
I can understand that a single flat mirror cannot ever appear brighter than whatever is being reflected. But why can’t multiple mirrors pointed at one spot have a total intensity greater than that of any one of the mirrors (or a curved dish that focuses the light)?
Multiple mirrors reflecting sunlight can indeed result in an irradiance greater than that of the Sun (this is how solar power towers work). But to do that, you need to cover more than a 0.5° circle of the sky with mirrors. The total irradiance can be as high as you want (up to covering the whole sky with mirrors, which would be equivalent to standing on the surface of the Sun) but the irradiance per angular area can never be higher than the Sun’s.
You can think of it as dividing a mirror of any shape into a bunch of flat mirrors. Each mirror can only show you a reflection of part of the Sun (which is exactly as bright as that part of the Sun) but you can have as many mirrors as you want showing the same part of the Sun, multiplying the light you receive from it (up to filling the entire sky once again).