The rainbow is something that occurs when the beams from the sunlight hit raindrop at a specific angle, the beam's constituent colours then become briefly separated (through reflection, refraction and scattering) for us to see. It typically lasts between a few minutes to an hour, unless of course, you happen to live in the Taipei's Yangmingshan mountain in Taiwan where the rainbow stayed a record-breaking 8 hours 58 minutes on November 30, 2017.
[Image from Pexels]Credit: A magenta textured glass
The seven colours of a rainbow are red, orange, yellow, green, blue, and indigo.
But if you look at the colours above you'd notice some colours are not there. Where is purple? Where is magenta?
[Public domain image]Source: A Rainbow
Well, the first answer is the colours are not amongst the colours of the visible spectrum of light.
The second answer is something to do with the way vision work plus colour mixing.
A ray of light comprised of individual units of light that are known as photons. Each photon has an energy and frequency. For instance, a photon of blue light has more energy than a photon of red light. In physics you can't change a red photon by mixing it with another photon. But you can do that in colour mixing in paints and arts.
But the human eyes can mix two light sources that overlap to produce another colour.
For example, if you manage to get two independent light sources- one is green, and the other is red, and mix and flash them on a surface, in the space where they overlap, you will see yellow.
[Wikipedia CC-BY-SA-3.0 by Meganbeckett27]Source: Copours of the visible light spectrum
This result is not surprising as a look at the visible colour spectrum of light shows that Yellow is somewhere between Red and Green light.
[Wikipedia CC-BY-SA-3.0 by Philip Ronan, Gringer]Source: Different waelenght of the visible light spectrum
The human eye can measure each light photon falling it purely by its frequency and wavelength. The photoreceptors are called cones.
For example, a banana appears yellow because wavelengths of between 570 to 580 nanometers hit the eye when someone looks at it. From above you can see that yellow lies in that wavelength range.
The human eye has about 6 to 7 million of these cones. These cones respond mostly to the three colours: red, green and blue. Though majority part of the cones say 64%, respond to red, with 2% for blue light, the rest responds to green light. The red cones are more sensitive to red and send a signal to the brain when the red light hits the eye. The same goes for the other two cones.
Others colours are seen much by a mixture of these three colours. This colour mix is similar to how the RGB monitor and TVs display every other colour through spectrum colour mixing of the red, green and blue pixels.
That means the yellow colour you see is a result of a mixture of both red and green cones firing. The brain then makes a decision that the colour is somewhere in between red and green and comes up with yellow which ideally is not what the eye "sees."
The Magenta Magic
So how can your brain tell that the dress you are looking at is magenta? Yes, the red and blue cones may fire. But somewhere in between is green. But the green cone is silent, which means the colour is not green.
The brain does its magic and viola; magenta is the colour you see.
Magenta is the only color that does not exist as a single wavelength of light. Some readers suggested that browns only exist as a mixture of wavelengths. But browns are dark shades of red and yellows and some browns can be generated by a low intensity single wavelength of red. For example 133:0:0 in the RGB scheme is brown (called maroon). Source
Conclusion
The truth is we "see" colours with our brain, that is why it is possible to see magenta colour even when it does not exist as a wavelength in the spectrum of visible light.
The other colours that we see are just stimuli of the visible light wavelengths which ranges between 400-700 nm that hits our cones. Oh yeah, magenta may not be a single wavelength, but our brain sees or perceives it as such by the way.
References
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