Why does a glass of tea get darker if it is left sitting out?
Because the water evaporates? Because you left the tea bag sitting in it? Because you live in a coal mine?
You might want to specify the type of tea and the exact process. I’ve never noticed the tea darkening effect myself.
If you mean the surface of the tea getting darker, it’s because of the tannins forming a scum on the surface. At least that’s why a nice British-style mug of hot tea with mile gets darker if you leave it sitting out.
It was white tea. There was no tea bag in the cup. The cup was covered so evaporation was minor. The tea started off as a light yellowish color that was almost clear. The next day it was much darker. And the day after it looked like a very dark black tea.
Maybe you’re talking about the “self mixing” properties of hot water cooling?
I typically get a cup of hot water, throw in a tea bag and leave it. Generally it “self mixes” somewhat (mostly you get a dual layer of water and super-saturated tea which mixes into a perfect cupa 
)
White and green tea leaves are not allowed to oxidize (or ferment, as they say in the tea biz) after they are picked; they are dried immediately so they don’t turn dark like black tea leaves.
When you make tea with the leaves, then, all those fermentable compounds are rehydrated and if you let the tea sit, they will oxidize, darkening the liquor. For this reason, you should only make as much green or white tea as you plan to drink right away. It’s not like black tea, which is already completely ferment, so you can make a big ol’ pot and put a tea cozy on it, and go back for a cup every once in a while.
Oxidation? or photo sensitivity?
oxidation
I learned from the instructions in a Brita filter package that tea made with tap water gets darker because (really simplifed) the tannin and other properties of tea bond to microscopic particulate in the water. Tea made with filtered water does not get as dark, no matter how long you let it sit, because the particulate matter has been mostly removed.
Another factor that can change the colour of tea is pH. (It’s probably not what the OP describes, though.)
If you add a few drops of lemon juice to black tea, it gets noticably lighter. On the other hand, if you add baking soda it goes dark (and disgusting).