Remember how the professors made a big deal about Harry not discussing his discovery about potions?

Perhaps school manuals are picked to contain only potions with magic ingredients, as a misdirection for people not wise enough (students) to try to figure out the "well-known secret", the same way Harry was at first.

But Harry's potion didn't release a lot of magic, it only released light (note that in the coin example, it was the non-magical coin that furnished the "heat"), so probably Harry used a bit of magic (like in Potions class) to "rearrange" the light without need of magical ingredients.

(Also, why wouldn't "wizard hair" count as a magical ingredient?)