The electromagnetic nature of light
So what is light?
Light is just one form of energy known as electromagnetic radiation. The same stuff as radio, TV and microwaves, just a different frequency. The light that we can see encompasses only a very small part of the entire electromagnetic radiation spectrum. This spectrum includes everything from low frequency radio waves up to extremely high frequency (and very dangerous) gamma radiation: Visible light covers a frequency range from around 5 x 1014 Hz for red light to 7.5 x 1014 Hz for violet light. That's between one-half to three-quarters of a million billion Hz! These very high frequencies are more conveniently described in the form of wavelengths. To obtain the wavelength of a particular frequency (or color) of light, divide the speed of light (approx. 300,000,000 meters per second) by its frequency. Red light would then have a wavelength of approx. 0.0000006 meters or 600 nm (billionths of a meter) in length. Visible light has a wavelength range of approx. 400nm to 700nm.
Outside of this range are the two well-known forms of invisible "light" - infrared ("less than" red) and ultraviolet ("more than" violet). Infrared is invisible but can be felt as radiant heat. Ultraviolet light is also invisible but has much more energy than visible light - as much as seven times the energy. (The scale above is very compressed spanning from 1Hz to 1 million billion billion Hz! Each graduation is 100 times that of its neighbor.)
But why does light damage fabric?
The molecules that make up different fabrics are held together with different molecular energies. Molecular glue if you like. Delicate fabrics' molecules are held together less strongly than those of tougher fabrics. If a photon with enough energy comes along and collides with such a molecule, it can impart enough energy to disrupt the molecule, creating two separate parts that are no longer the same material. This is the process that, if repeated often enough, will cause discoloration and possibly even destruction of a delicate fabric. It is also why ultraviolet light damages our skin while visible light has no effect. The energy in visible light is not sufficient to cause molecular disruption in our skin.
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