Most touchscreens these days use something called “capacitive touch”.
Every pixel has some electricity being pushed in and out of it over and over again, quite fast. When your finger is near a pixel, it makes this easier to do, as the electrons in your finger can (sort of) freely move.
The screen detects how easy it is to move electricity in a particular pixel, and so it knows which pixel your finger is near.
Couple of ways.
The most straightforward to understand is resistive. There’s two rows of thin nearly invisible or actually invisible wires going vertically and horizontally on two films. Press, wires make contact, and electronics knows. Cheap and durable. You see it on stuff like industrial touch screens and kiosks like ATMs where durability is important, accuracy doesn’t matter as much, maybe people with thick gloves need to press buttons. Also on the cheap pen signature pads.
The more common one for cell phones and monitors is capacitive. Similar grid of wires, but by sending a high frequency signal through them they can detect when a finger is near by how it interacts with that signal and changes the capacitance in a region just above the screen. Nice cause it works on rigid glass, and is pretty precise. It doesn’t work with gloves that aren’t designed for it though, and can get messed with with water drops (which have a similar capacitance to a finger since people are mostly water)
There’s also other interesting ways that are more rare with niche applications. Such as acoustic touch panels which basically use sonar through the glass to see where sound gets absorbed by a finger touching the panel. Infrared/laser break beam grid just above the surface hidden in a frame around the outside. Seen one that when you pressed down on it a camera behind the screen would detect the shadow of your finger.
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