The lens are coated with a very special compound that is photochromic – meaning that it changes color when it is exposed to UV light. This is a very common thing in chemistry – many molecules react when exposed to UV light.
When UV light hits the compound, it changes shape, and that new shape is darker than the shape than the original shape. After a time without UV exposure, the molecules revert to their original, clear shape.
I dislike how the other replies basically just reformulate that they get dark in light because they get dark in light.
Some chemicals are very stable. Gold, for example. It really takes some effort to make it oxidize, e.g. Aqua Regia, a *very* strong acid, will dissolve gold. On the other end of the spectrum is stuff like lithium, sodium and aluminium. It takes extreme effort to *not* make it oxidize, because it’s so damn reactive. Nevermind using an acid, they’ll happily burst into flame on contact with plain water or even just air!
Silver is balancing riiight inbetween, a little indecisive. You can oxidize/dissolve silver with something like nitric acid, although it’s a quite slow process. Once dissolved, as silver nitrate, it remains a little indecisive. You only need to introduce the tiniest bit of energy via for example a bright light to scare it back into metal again. Silver’s ability to go back and forth between these states with very little energy involved is what photochromic lenses use. I don’t know the exact chemicals used in lenses precisely, but this is the sort of mechanism they use. A bit of energy via UV light forces something into an opaque substance, but once that source is removed it quietly dissolves again.
First, it isn’t a coating – the silver salts used in transition lenses are in the glass itself. This is important, because the reversibility of the reaction is really important – you want the glasses to go clear again.
Silver salts (like silver chloride) form with electrons that are a long way from the nucleus of the chlorine atom. If you hit those electrons with a high-energy UV photon, it can push an electron from the choride ion to the silver ion, which becomes a silver atom – this makes the silver atom opaque, and as more of the silver ions are hit, the glass gets progressively darker with more and more silver metal.
This happens in a solution, too – expose silver chloride solution to light, and it will change colour, because silver ions are turning to silver metal. In a solution, this reaction is not reversible, because the silver precipitates out. But the silver ions and the chloride ions in glass lenses cannot move, so they are still in the same position next to each other. Eventually the electron that was pushed to the silver ion will emit the UV energy it absorbed, and jump back to the chloride ion. Once that happens, you don’t have a silver atom any more, and the lens goes back to being clear.
There is a delicate balancing act between clear ions and silver metal, and that balancing act is determined by the Schrödinger equation, which is quantum mechanics. That part isn’t ELI5.
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