Chemical reactions need a certain amount of energy to happen. For things that happen spontaneously, that energy can come just from the ambient temperature. The material the fillings is made from gets the energy from the light, which knocks electrons and atoms around causing the reaction to happen and you’re left with a hardened filling.
The chemicals inside it enter a reaction, which results in new material that is solid. Much like when you take a glowstick and “activate” it (by breaking glass vial inside and mixing two liquids), the chemical reaction causes it to start glowing.
UV reactive materials can be found in many parts of our world. UV reactive resin, for example, is used in construction or (more recently) 3D printing.
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