I know that if you held an infrared remote in front of a digital camera, it'll flash a blue/purplish light when you press the buttons. Why?
(Image by Zombie Rider.)
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This happens because the spectral response for each red/green/blue pixel in cameras don't exactly match the spectral response of the receptors of your eyes. For example, check here and here, and compare them to the human eye (and read the whole wiki article for interesting details on human color perception).
What digital cameras do, is to try to mimic your eye+brain's perception. Of course, since the material of a CCD and your body are so different, it's easier to just do it approximately. And in any case, you can't show all the colors you see in a normal display because the pixels in them also only mimic your perception (see the CIE chart at the end of the previous wiki article). This means that in many cases the colors you see and the colors you get in a photograph are only similar and, in extreme cases, really different.
This is specially the case of infrared ligth (as in your remote control), and at both edges of your color range. I tried to get a picture of a 400nm (violet) laser that had a great color, and only got a pale blue on the screen.
On the other hand, since different cameras have different filters for their color pixels, what color you get also depends on what camera you use. When I took a picture of a remote with a cheap webcam I got red instead of your blue/purple. It is a great way to know if your remote works, though!
The imager chip has red/green/blue filters over alternate pixels.
It's difficult to design filters that are very transparent in the wavelengths you want and completely blocking outside. One problem is they typically switch back on again at twice the wavelength, for blue this is beyond the red and in the near IR so isn't normally a problem.
But if you have a strong narrow IR source eg 800-900nm in the Kodak ccd below, it would transmit through the blue filter and show up as blue in the image
There is generally an infrared blocking filter as well which blocks everything beyond about 650nm but your's obviously doesn't work too well.