<snip> I wonder how many lumens a reflection of the sun from one of those small mirrors would be.<snip>
Per a Navy manual, a 3x5" glass mirror on a bright sunny day is 8 million candlepower. The actual number is going to be a function of the sun elevation, atmospheric clarity, mirror reflectance, and the sun to target angle included at the mirror.
My calculation:Aiming at the horizon, assuming a mirror reflectance of 0.85, and the sun directly overhead (beam 45 deg off mirror surface normal), using a standard solar flux atmosphere model[1], I arrived at 4.4 million candela (the modern unit for candlepower) for a mirror surface of 6 square inches (a bit more than the net area of a 2"x3" mirror). That is in rough agreement with the Navy manual, after accounting for the different mirror size. However, the candlepower is so impressive because the beam is so small, not because of the power involved.
A candela is a lumen/steradian, and using 0.5358 deg for the sun diameter (median diameter over the year), all that power is going into a beam subtending only 1/14,560 of a steradian. So, to get lumens, I multiply candelas by 1/14,560, getting 300 lumens.
So, at high noon, beaming to the horizon (in any direction) we are talking 300 lumens - high, but not impressive per se. The reason it is so bright is that all those lumens are being crammed into 1/14,560 of a steradian beam, hence the 4.4 million candlepower.
[1]
http://stjarnhimlen.se/comp/radfaq.html#10