Light is made of up of an electromagnetic wave. In order to go forward (propagate) it needs to be able to build an electric field. This is really hard in a metal, which basically short circuits that. Thus the electric field is quickly reduced to 0 (Volt/meter). This effectively stops light in its path.
The “short circuit” can be seen as a reverse voltage. It cancels out the incoming wave. The reverse voltage will also propagate in the opposite direction: The reflection.
Fun fact: If the material is thin enough, some light can tunnel through as the electric field is not completely reduced to 0 V/m. In the end, light is also a particle and will either reflect or tunnel through then. The tunneling effect is used in two-way mirrors (and other electronics)
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