I'm sorry, I can't find the specific source myself, but I remember this story pretty well as being in the Romance of the Three Kingdoms (三国演义). I believe it was during a battle between Liu Bei's forces and Cao Cao's -- two of the three major warlords during the end of the Han Dynasty, in the early 3rd Century AD. I can't find the exact instance in my copy right now, so I apologize for this being unhelpful. Also, keep in mind that ROTK is a heavily fictionalized and romanticized account of the actual events of the Three Kingdoms period -- it's likely that the story of the mirror shields is more folk tale than truth.

If nothing else, the use of these mirror-shields to stop a charge is depicted in the film Red Cliff, and a clip of this scene is at this link.. Hardly an authoritative source though.

There is also Archimedes and the Burning Mirror which Mythbusters also did a thing on.

What you remember is probably a 1959 movie:

Pursued by the Egyptians, who were sent to finish him off, Solomon thereafter devises a plan. He lines up the remnants of his army on a hill, prompting the enemy to charge. The Israelites, who have arranged themselves to face east, then use their highly polished shields to reflect the light of the rising sun into the Egyptians' eyes. Blinded, the Egyptians are prevented from seeing the chasm in front of which the Israelites have positioned themselves, and the entire army rushes headlong over the edge and falls to its death.