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I'm studying the refraction in optics.

If a red light monocromatic beam of red light (700 nm) passes from air to water it becomes with a wavelenght of aprox 526 nm.

So, my question is: How is going to see this beam a diver? Red (700 nm) or something more like green (526 nm)? (Let's suppose that the diver isn't wearing glasses).

I think that he is going to see the beam green? I'm a little confused...

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Only frequency remains unchanged. Speed and wavelength change while transmission. –  Awesome Apr 28 at 9:31
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Yeah, frequency remains unchanged for refraction between any two media. And since colour depends on frequency, not wavelength, the colour observed in any medium will be the same. –  mikhailcazi Apr 28 at 9:43
    
I'm confused... –  Marc C Apr 28 at 10:02
    
color vision [′kəl·ər ‚vizh·ən] (physiology) The ability to discriminate light on the basis of wavelength composition. And in fact, in my physics books, all the light spectrum tables are listed by wavelenghts –  Marc C Apr 28 at 10:03

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up vote 10 down vote accepted

You will see it the same, regardless of the refraction index of your medium. The reason is as simple as that, when the light hits your retina, it will be travelling through the interior of your eye, so the only refractive index that matters is that of the eye.

What is what we actually detect, wavelength of frequency? Frequency is the one related to energy, so my feeling is that that should be the one influencing chemical reactions, that is, at the end, the way cones can detect light.

Indeed, the vitreous humour (the interior filling of the eyeballs) looses water with age, to the point of getting deatached from the retina, something very common among old people (Wikipedia says 75% of > 65). The main consequences are visual artifacts, but no one has claimed colours suddenly look different.

Physics books quote wavelengths because those are usually what one measures in the lab in the optical range. Plus, the numerical values are (and this is subjective) more convenient.

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Huge! This the sort of answer I was looking for, thank you very much. And in the same way, refering to Doppler effect, if I have this same monocromatic beam and I send it to a car coming, it's reflecting in another frequency, so, shouldn't I see the beam of a different colour? –  Marc C Apr 28 at 10:58
    
You will, but the difference is a factor of $\frac{v}{c}$, that is tiny for reasonable velocities. You can measure it, but not see it with the naked eye. –  Davidmh Apr 28 at 11:03
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Except, as the joke goes, an example of relativistic Doppler effect are cars: we see the lights white when they come towards us, and red when they go away. –  Davidmh Apr 28 at 11:12
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By the way @marcC the wavelength shift of "light reflected off a moving car" is NOT typically what the police use in their "laser Doppler" equipment to measure the speed of cars (instead they use LIDAR- measuring the arrival time of a series of very short pulses. This is still the Doppler effect but not at the frequency of light.) –  Floris Apr 28 at 11:16
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Just to be explicit: photodetection at the rods and cones of the retina is a quantum process, which means photons are detected, not waves. The energy of a photon is unchanged snce the frequency hasn't changed. –  Carl Witthoft Apr 28 at 11:43

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