People see colors because of the cone cells in the eye. There are 3 types of cone cells, that are most sensitive to red, green and blue light respectively. The color that you see is determined by the relative strength of the signals that these cone cells give to your brain. When both blue and red signals are strong, you perceive the color as purple. That’s why you can add red and blue lights to get purple. The reason that the short end of the electromagnetic spectrum appears violet/purple is that the blue cone cells contribute a little bit to the red signals that your brain receives, in the absence of a green signal. (I am simplifying things here, you’ll need to drill deeper into Opponent Process to get the full picture).
Relevant Wikipedia links:
https://en.wikipedia.org/wiki/Violet_(color)#Optics
https://en.wikipedia.org/wiki/Opponent_process
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