I was in for a blood test this morning, so I got to idly wondering - as you do - why do veins look blue when blood is most definitely red? Well, of course I'm not the first person to wonder that, and the answer was not hard to find, in various different formulations.
It turns out it's all to do with how we perceive colours and how deep under our skin our veins are. The first thing to know is that we see colours when light of that colour hits (either directly or as a reflection) our eyes, and that things of different colours absorb those parts of the spectrum making up white light from the sun or electric lighting, and reflect back the rest.
You probably already know that different colours of light have different wavelengths, and you may also know that the red end of the visible spectrum has a higher wavelength and the blue end shorter. Red light, therefore, with its longer distances between peaks and troughs, is less likely to be deflected and scattered by the materials it travels through (including skin), and it can easily penetrate the 5-10mm to where our larger veins are located. There it is largely absorbed by the red veins it encounters (technically, by the hemoglobin, the protein that makes our blood red). The shorter-wavelength blue part of the spectrum, on the other hand, is much more easily deflected and does not penetrate as far (and is therefore mostly reflected back).
Pulling all this together, when light hits your skin, a mixture of colours will be reflected back, but where there are veins under the skin, relatively little red light is reflected back (because it has been absorbed by the red veins), and your veins appear blue compared to the rest of your skin.
At this point, you are probably regretting even expressing an interest, because some of this stuff, although quite logical when you think about it, does seem a bit counter-intuitive. But the bottom line is that, although your veins are in fact red (being filled with blood and all), they appear blue when seen through the skin because of the relative wavelengths of the colours, and the extent to which the different wavelengths are absorbed or reflected back. Got that?
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