The Real Reason Flames Don't Have Shadows
Uh, why don't flames have shadows? Like, I mean, hello, it's kind of freaky. But it has everything to do with what a hydrocarbon flame is. When you look at a candle flame, the part you can see is not a gas, and it's not a plasma, believe it or not.
The part you can see is a solid. A flame is a chemical salad full of wax and oxygen molecules that are burning. Carbon dioxide and water vapor are products of the combustion, as well as hot air and unburnt solid fuel particles that are so hot they're glowing incandescently. That's where the light comes from.
But all of this stuff is not very crowded. In fact, a flame is about only a quarter as dense as the surrounding air. So, light can pass right on through. Whatever shadow is created can be easily filled in by the glow of the flame itself.
What the flame mainly does to light can be revealed by using a light that is brighter than the flame. Light travels at different speeds through media that have different densities. So, passing from the hot flame to the cooler air, we get ghostly distortions of intensity that are the only evidence that anything's there.