The clear plastic has a layer of tiny silver halide (commonly bromide) crystals. When you take an xray exposure, you flood the object with xrays, and most of them pass through the object. Some of them get scattered by the object. Dense things, like bones, scatter more than soft things, like fleshy bits, so fewer xrays make it all the way through to the film behind the object. The places where the xrays strike the silver halide crystals on the film, a chemical reaction takes place that activates the crystal (it gets charged). This leaves it susceptible to a process called chemical reduction (you get a bit of black metalic silver) at that spot when it’s placed in the developer. In the places where the xrays didn’t make it through the object, you have less black metalic silver formed, and so it is more transparent to light.
No printing, there’s just less of a blackening chemical reaction in the places where fewer xrays hit the film.
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