A little over 2,200 years ago, the Roman navy attacked the Greek port city of Syracuse. According to some ancient historians, the Greeks defended themselves with an ingenious weapon called a "burning mirror": a polished copper surface curved to focus the Sun's rays onto Roman ships, causing them to catch fire. However, we have several reasons to suspect that the story of the burning mirror is just a myth and the Greeks of Syracuse never really built such a device.
First, the ancient Greeks were not technologically advanced enough to make such a device. A mirror that would focus sunlight with sufficient intensity to set ships on fire would have to be several meters wide. Moreover, the mirror would have to have a very precise parabolic curvature (a curvature derived from a geometric shape known as the parabola). The technology for manufacturing a large sheet of copper with such specifications did not exist in the ancient world.
Second, the burning mirror would have taken a long time to set the ships on fire. In an experiment conducted to determine whether a burning mirror was feasible, a device concentrating the Sun's rays on a wooden object 30 meters away took ten minutes to set the object on fire; and during that time, the object had to be unmoving. It is unlikely that the Roman ships stayed perfectly still for that much time. Such a weapon would therefore have been very impractical and ineffective.
Third, a burning mirror does not seem like an improvement on a weapon that the Greeks already had: flaming arrows. Shooting at an enemy's ships with flaming arrows was a common way of setting the ships on fire. The burning mirror and flaming arrows would have been effective at about the same distance. So the Greeks had no reason to build a weapon like a burning mirror.