Question

Why is water in a glass cup quickly warmed in a microwave oven, but the glass cup itself warms much more slowly, if at all?

Answer 1

Microwave ovens use very high frequency radio waves that are designed to be absorbed by water, fat and sugar molecules. The waves pass right through glass and so do not heat the glass.

Explanation:

Things absorb waves at specific wavelengths or ranges of wavelengths. We see this in colored objects; if something appears red, for instance, it's because it absorbs shorter wavelengths of visiblle light leaving the long red wavelengths to pass through or be reflected. Different things appear to be different colors because they absorb different visibke wavelengths.

The same thing happens with microwaves, which are in effect very high frequency radio waves. Water, fats and sugars absorb a certain range of wavelengths while nonmetallic container materials, like microwave-usable glass, let those wavelengths pass through to the food inside. So the food that contains water, fats and sugars is where the absorption happens; the absorption becomes its own heat source within the food.

See here as well.