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While it's on its beaming red and looks menacing . Is there any harm that can happen to your eyes while it's on looking at it other then drying out eyes from heat?

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No, your stove is fine to look at.

If it is actually an induction stove, then the red would just be a light to let you know it's on. The actual induction heating won't make the cooktop glow red.

You might just have an electric glass/ceramic cooktop, though, in which case the heating will make it glow red, but it's still safe. Things glowing from heat are just emitting red and infrared light, pretty much the same as some glowing coals from a fire, not at all harmful to look at.

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Assuming it is or an actual induction stove with a red backlight.

Your concern is likely because an open microwave source (eg a microwave oven with a damaged case and/or a defeated safety interlock ... or a powerful radar or communications transmitter) in the power range cooking devices have is well known to be an actual eye safety hazard.

There is an important difference. While both kinds of devices use an electromagnetic field with hundreds of watts of power, the frequency is different by several orders of magnitude.

With induction stoves, a frequency in the area of tens of kilohertz (high enough to avoid making loud audible noise!) is used, and probably in the single megahertz range for very modern all-metal induction stoves. EM radiation at these frequencies can get ferromagnetic metal extremely hot quickly, but it has very little effect on water or just lightly electrically conductive tissues. The field from an all-metal device might be somewhat more "aggressive" towards non-magnetic or even non-metallic conductive materials (since it likely works by using the load as a shorted transformer secondary rather than by causing magnetostriction) - still much safer than a powerful, microwave source.

RF energy in the 2.4 gigahertz range is what microwave ovens use. This will heat anything in its path that absorbs it - and water is very good at absorbing RF especially in this frequency band. Whatever is heated does not need to be magnetic or even conductive - pure water is hardly conductive and will get heated just as well, and oil is a great insulator and will get heated quickly. People and their eyes are made with plenty of water. Even here, most of the damage is thermal, not "radiation damage" of any kind: A 1 watt WIFI transmitter - which uses the exact same radiation as a microwave oven - is harmless to your eyes, and also will not cook anything around. An 800 watt microwave oven is very different in both aspects. Actually, a visible light source at an actual 800 watts of output power would be an eye safety hazard just as well.

Also, induction cooktops are usually designed to not blindly transmit radiation into the surrounding space when there is no load (it would actually put strain on the electronics to do so), while a magnetron will always transmit at full power even if it has not much to heat (actually, running one in an enclosed, reflective space like an empty microwave oven WILL strain it too, since the energy has to go SOMEWHERE).

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