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When I think of white light, I'm imagining a combination of all 7 colors of light but I believe that since light has wave nature I can say that at some point that the probability density of red light is more than that of violet light and vice versa right? My doubt is that since both have different probability densities of different colors they should emit different colors right? But then why do we still insist on calling both of them white light or actually why does it look white to us?

Also I don't think I'm wrong in saying that red light and violet light have different maximas and minimas as we can see so when we pass white light through a Young's double-slit experiment (YDSE) setup. Violet light's maxima closer to the central maxima as compared to red light maxima. In fact I think that light should've appeared to us the way it does when we let white light pass through YDSE (except for the central maxima since that's only the case here since Δx = 0 in this case, Δx being path difference.).

YDSE_WITH_WHITE_LIGHT

EDIT 1:-

Kindly ignore the '7 colors' part since as gandalf61 pointed out that our eyes can see many more colors than just the 7 colors.

The main point of my question is since every color present in white light has a different probability density at some point, every point in light should emit a different color depending on the color mixture we obtain there.

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    $\begingroup$ Have a look at the complexity of the word "color". hyperphysics.phy-astr.gsu.edu/hbase/vision/colper.html $\endgroup$
    – anna v
    Commented Feb 17 at 13:21
  • $\begingroup$ Thank you @annav , I've somewhat understood what's going on. $\endgroup$
    – Gauransh
    Commented Feb 17 at 14:05
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    $\begingroup$ watch youtube.com/watch?v=uYbdx4I7STg ..it's a biology question. $\endgroup$
    – JEB
    Commented Feb 17 at 18:08
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    $\begingroup$ It's important to remember that the colors that we perceive have as much to do with our biology (eyes) and our neural processing (visual cortex, etc.) as they do with physics. $\endgroup$ Commented Feb 19 at 15:59
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    $\begingroup$ I suggest that you have a look at Berlin and Kay's. It seems that colours have psychological reality (linguistic reality?): some languages have only 3 colour terms (light, dark, and red); others have 4 (light, dark, red, and either yellow or green), but none have yellow/green without red. $\endgroup$ Commented Feb 19 at 23:52

6 Answers 6

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The retina of the eye contains rods and cones, which are the actual light-sensitive components. Cones see colour and rods don't so I'll only talk about cones here. There are three types of cone: L, M, and S. Each can detect light over a range of wavelengths/frequencies/colours, with peak sensitivity at one colour and lower sensitivity at other colours. There are graphs in the wikipedia article at https://en.wikipedia.org/wiki/Cone_cell.

Every colour we see triggers a particular combination of levels for the three types of cone. If only L is triggered you will see a deep red. If S is triggered most, with only a little L and M you will see a deep blue. When we look at a "white" object in good light (e.g. daylight), a particular combination of L, M, and S is triggered, and we call that sensation "white".

The cones are closely packed in the part of the retina we use to see most clearly. Our brain does not separate the signal from adjacent cones in a way that lets us interpret it as coloured spots close together. Instead it interprets the signals as the images we are used to seeing when we look at things, in order to help us live our lives.

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    $\begingroup$ I'd mention the processing that occurs in your brain to interpret those signals also. Get a cheap pair of the old 3d glasses with one blue side and one red side and wear them for a few minutes. Now take them off and look at a white wall and alternate closing each eye. Each eye will see it as a different color for a bit because your brain adjusted to the glasses. $\endgroup$ Commented Feb 19 at 19:44
  • $\begingroup$ @JasonGoemaat isn't that adjustment happening in the retina? I do not recall the exact name of it, but it was either that there was some suppression happening, or the cells becoming fatigued from a repeating stimulus. $\endgroup$ Commented Feb 20 at 12:15
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When I think of white light, I'm imagining a combination of all 7 colors of light ...

The idea that there are only seven colours is a misconception that probably originates with Isaac Newton's division of the spectrum of daylight into red, orange, yellow, green, blue, indigo and violet. This is an arbitrary convention - the human visual system can distinguish far more than 7 colours, and there is no clear and objective borderline between, say, green and blue.

The definition of "white" depends on context. A simple definition of white light might be that its spectrum contains equal energies at each visible wavelength. However, light with this spectrum (know as standard illuminant E) has a distinctly red/orange tone when compared to the visible spectrum of daylight (standard illuminant D65). On the other hand, a white surface is defined as one that reflects all visible wavelengths equally - and so it is in fact achromatic and its apparent colour will depend on the spectrum of light with which it is illuminated.

Different wavelengths of light produce different spacings of maxima in a double-slit experiment. So if you use some version of white light (or any light that is not a single wavelength), you will see a superposition of the interference patterns of all of its constituent wavelengths. All wavelengths have a central maximum, so the centre of the interference pattern appears white, and the fringes for different wavelengths become more dispersed out as you move away from the centre. In a lens this effect would be called chromatic aberration.

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  • $\begingroup$ Ty for your explanation! But unfortunately your answer still doesn't answer the main point of my question, there may be however many colors that make up white light, but since all of the have different wavelength and different probability densities at a given point, every point should emit a different color which wouldn't be white, then why does light appear to us as white? $\endgroup$
    – Gauransh
    Commented Feb 17 at 13:17
  • $\begingroup$ Also why exactly do the fringes spread further and further apart? In a lens it's cuz of chromatic aberration as you stated, but what's the cause of it YDSE? shouldn't the fringe width be the same that is λD/d (λ -> Wavelength, D -> distance between slits and screen, d-> distance between slits individually) – According to Huygen's principle intensity would decrease inversely as slits would emit non planar wavefronts but why would anything affect the fringe width except for the variables in the formulaw $\endgroup$
    – Gauransh
    Commented Feb 17 at 14:38
  • $\begingroup$ @Gauransh I am not sure what you mean by "probability densities" in a beam of light. Maybe you are confusing the waves in the electromagnetic field that make up light with the probability amplitudes of quantum wavefunctions ? As for YDSE, fringe spacing is proportional to wavelength, so if the incident light contains a mix of wavelengths you will see a a blurred pattern of fringes with different spacings superimposed on one another. $\endgroup$
    – gandalf61
    Commented Feb 17 at 14:49
  • $\begingroup$ Why can't I mix up probability amplitudes of quantum wavefunctions with EM waves? Wait right I am confused, wave nature of particles are probability waves and wave nature of light was supposed to be EM waves, how can something exhibit two wave natures at the same time? Are they both the same thing? As for YDSE, I misread what you typed and that's what caused the confusion mb. $\endgroup$
    – Gauransh
    Commented Feb 17 at 16:50
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    $\begingroup$ Newton, the last magician, invented Indigo because he believed that there should be 7 colours by analogy with the 7 notes of the major scale. $\endgroup$ Commented Feb 19 at 9:05
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You're right that there are local fluctuations in the relative presence of different frequencies of light in white light (e.g. sunlight). What I think you're missing is that the fluctuations are distributed in time as well as space. The frequency of visible light is in the hundreds of terahertz, while your visual system can only see changes at a rate of tens or hundreds of hertz, so everything you see is an average of roughly a trillion independent random fluctuations. That's more than enough to wipe out any visible randomness in the color.

(You can make the same argument about spatial distribution, but the ratio there is much smaller—cones are a few microns across, while the wavelength of visible light is around 0.4 to 0.7 microns—so the argument is weaker.)

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    $\begingroup$ +1 IMO this is the only answer so far that accurately addresses the original query. $\endgroup$ Commented Feb 18 at 20:20
  • $\begingroup$ Thank you for your answer! $\endgroup$
    – Gauransh
    Commented Feb 19 at 4:05
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The human perception of color is profoundly complex and wavelengths are only a small part of the whole picture.

One can perceive as "white" even a single wavelength. If you illuminate your whole environment with monochrome light (no matter what wavelength as long as it is visible) your visual processing system will adapt to perceive the brightest spots as white, the least bright spots as black and everything in between as shades of gray.

In a less extreme situation where your environment is illuminated with some mix of wavelengths and intensities that can be considered "white" by however liberal standard, you will perceive as white any spot that triggers a retina response analogous to the light source. This is why a piece of white paper looks equally white in either a daylight or in a candle light. If the light source itself is not in your visual field, your eyes(and brain) will adapt to see "white" using various other hints from what you see.

BUT! triggering a particular retina response is possible in numerous ways. For almost all definitions of "white", you need to mix only two wavelengths to make the same "white". Our usual color-representing systems (displays, printing processes, photography, etc...) usually mix 3 different "basic" colors that makes them able to represent wide variety of colors.

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    $\begingroup$ One of the most interesting things to me about our perception of color is how much of it is imaginary. I used to have room which was painted green. The hallway outside was painted a muted yellow. If you sat in the room at a certain time of day, the hallway would appear to be painted pink. And it wasn't a temporary effect. You could walk out, confirm that it was yellow, go back in and see the same shade of pink again. $\endgroup$
    – JimmyJames
    Commented Feb 19 at 15:40
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A few preliminaries:

  • The quantum mechanical model of light is not necessary here. While it can fully explain the wave behavior of light, it is harder to understand, and the classical wave model of light has sufficient explanatory power. Forget quantum mechanics (and thus probability distributions) for now.
  • In the classical wave model, you can imagine that at every point in space there is an oscillating electric field. The visuals we perceive depend on how this field oscillates at a point of our retina. Its frequency determines the color, and its amplitude the intensity. If the oscillation is harmonic, we perceive a spectral color, otherwise we perceive a mixed color.

Now with these out of the way, let's get to your misconceptions. Under normal circumstances, light has no minima and maxima like in the double slit experiment. If you have a pure spectral orange light, like from a sodium street lamp, then there will be no alternating patterns of orange-dark-orange-dark-... . While the electric field due to the orange light wave has minima and maxima, that is not what we perceive. We emphatically cannot perceive the strength of a static electric field with our eyes. What we can perceive, however, is the frequency and amplitude of an oscillating electric field. And while the electric field has maxima and minima at different points in space, the frequency with which these change is the same at every point in space, so we perceive the same orange color everywhere. And other than the fact that the intensity of a light source shrinks with distance because the energy is spread out over a larger area, there are also no changes in the amplitude of the oscillation, so we also do not have visual maxima and minima of the intensity.

The pattern we see in the double slit experiment is something entirely different. At the maxima of this interference pattern, the electric field is still not stationary. For instance, where you see a red maximum in the pattern, the field oscillates with the frequency corresponding to red, and we can perceive this oscillation. Where there is a minimum in the pattern, the electric field is stationary, though: it does not oscillate at all, and that is why we can't perceive it.

Now what does this have to do with your white light? White light is nothing more than light of different frequencies mixed together. The red part makes the electric field oscillate with the red frequency at every point in space, the orange light does the same with the orange frequency, and so on with every spectral color there is. At every point in space, there is an oscillation of the electric field with every frequency. While the spatial waves corresponding to each frequency do have minima at some points in space, these minima change to maxima and back at the corresponding frequency, and we don't perceive the minima and maxima, just the frequency with which they change. So there is no point in space where any color is "dark", because there is oscillation everywhere - unless we see interference patterns, which require specific conditions to occur, like a double slit with coherent light.

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  • $\begingroup$ Thank you for your answer, right it does make much more sense classically. $\endgroup$
    – Gauransh
    Commented Feb 19 at 4:03
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To misquote Wittgenstein, what would a mixture of all colours look like if it didn't look white? Remember that "white" is the name that we give to a sensation; Nature doesn't "do" white.

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