~50 years ago a greek historian tested it and it worked (one time with small boat in a water basin and one time on some wood far away from the people who hold the shields)

And it would be nearly impossible to get enough guys holding enough mirrors and get them all to aim a single spot on a moving object far away. Maybe if you drilled a unit for a couple years...
Syrakus was really big city and i doubt they would have problems to find enough people to hold the shields.

The theory of using sunrays to make a fire is true, but if they were able using this system to make a warship catch fire back in the ancient days of rome and Quart Hadast is still (and imho will be forever) debatable.