Yes, staring at a microwave will damage your eyes while it's running. You know the eyes are subtle and tender. The microwave, when we use it, it will generate abundant radiation. You know the foods are heated by this kind of radiation within the microwave, so you can see, how strong of the light wave is. However, if the oven is closed when we use it, most of the strongly light wave will not escape from the inside. If you keep it in a certain safe distance, no issue will happen for you to use it. The microwave will lead moisture loss, the eyes will be dry when you near it at working time.
Most people believe that looking at microwave when it is on will damages eyes. In fact, it not bad. The Microwaves do not emit radiation. And when you use it to heat up food, it is non ionizing radiation with such a low frequency. They are not so harmful as radio waves. And they do not use UV rays, X rays, or gamma ray. The Microwave only cause electromagnetic radiation that can cause you any harm.
Usually,the working frequency of household microwaveis about 2450MHz. Cystalline lens of eyes are the most possible part to be hurt under this working frequency. Therefore, when microwave is working, it might damage eyes either looking into it or just staring it for a long time. Mostly seriously is light harm is very possible to cause cataract. Such light harm includes X-ray, ultraviolate radiation, computer tomoscan, high tension wire, microwave, electric blanket and TV.
So we should be very clear about how to use microwave and try to avoid as much hurt as possible.