What Is Light?

Sharpless 2-106 (Gemini Observatory/AURA, right; left: copyright Subaru Telescope, National Astronomical Observatory of Japan; All rights reserved)
In most texts that discuss light, what is often referred to is actually that very narrow band in the electromagnetic spectrum that stretches somewhere between wavelengths of 400 nm to 700 nm. That's from the colors violet to red.
It's called visible light because, well, its behaviors are easily observable through our naked eyes. You can see what really happens when rays of visible light undergo reflection, refraction, diffusion, interference, and diffraction. When you look at the mirror, see a rainbow, marvel at the tail of a peacock, or observe the bottom of a pool appear shallower than it actually is, you're witnessing the behaviors of visible light.
So if that's visible light, then what is invisible light? Invisible light may actually refer to all members of the electromagnetic spectrum whose behaviors cannot easily be perceived by the human eye. This should therefore include radio waves, microwaves, infrared, ultraviolet, X rays, and gamma rays.
While it is difficult to observe non-visible light through our naked eyes, their applications are still familiar to us.
For instance, radio waves allow us to communicate with our associates who may be located in another city or even somewhere across the globe. Cell phones, which is fast becoming (if not yet) the most ubiquitous device in the world, make use of radio waves.
Operate a remote on your TV, and most likely, you'll end up using light in the infrared. Walk out into the Sun and stay there for a long time. Pretty soon, you'll get a sunburn, courtesy of ultraviolet light.
Therefore, if visible light is the small band in the electromagnetic spectrum whose members can be easily perceived by the human eye while invisible light refers to all the other members in the electromagnetic spectrum that cannot, then it would be safe to conclude that the answer to the query, "What is light?", is the entire electromagnetic spectrum.
You might want to learn more about specific bands in the electromagnetic spectrum that are non-visible in your quest to find a deeper answer to the question "What is light?". We've got some nice articles here in Universe Today.
Why don't you start with articles about infrared and its applications in astronomy?
There are also interesting stories from NASA and PhysicsWorld:
NASA Infrared Images May Provide Clues About Mt. St. Helens' Eruption
High Performance Near Infrared Camera
Here are two episodes at Astronomy Cast that you might want to check out as well:
Infrared Astronomy
Optical Astronomy
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