This is an example of an inverse problem in perception. The light that finally reaches our retina is the product of three things: the nature of the illuminant (what wavelengths are emitted), the surface reflectance properties of an object (what wavelengths are reflected), and the medium through which they travel (what wavelengths are filtered). Here is an illustration (panel A).

So basically there are three physical quantities that the visual system needs to recover from a single value (what actually arrives at your retina). That means that there are lots of possible combinations that can produce the exact same input to the visual system! If more light falls on our retina, how can we tell if it's because the light source got brighter, the object changed color or became more reflective, or if the air became less foggy?

Fortunately, there is a lot of information available in the world that helps us. For example, if there are several objects in a room, then we can see different surface reflectances under the same illumination (holding one of the variables constant). We also can make lots of assumptions based on our prior experiences, such as light usually comes from above etc.

When everything goes well, we achieve what is called luminance and color constancy that is -- we experience objects as having consistent surface reflectance properties despite changes in illumination. This is a very reasonable goal for our visual system: very few objects in the natural world quickly change color, but the illuminantion and medium (e.g. fog or mist) changes all the time every day.

These assumptions of our visual system can lead to fantastic illusions where constancy fails. Classic examples are when you see a sweater in a store under one illumination and then go outside and it's a completely different color. This is in fact the explanation for the dress illusion from a few years back -- depending on your assumption of the color of the light in the store (yellowish or whitish) the dress appears either blue and black or white and gold.

Here are a few other fun examples:

Because we take into consideration that shadows reduce the amount of light reaching our eye, we assume that surfaces in shadow are actually lighter than they appear. Here squares A and B are physically identical (exact same pixel values) but one appears much lighter than it is. Here is a color version and here is a version that shows the effect of the illuminant.

I find this one the most compelling -- the chess pieces are actually identical (not black and white); the only thing that is different is the pattern of the fog (here is the same image with no background/foreground).

Here is an example of the "light-from-above prior". This is actually the same image, just flipped 180 degrees. You can download it and rotate it yourself (or rotate your phone!) and you will see the one that sticks out become the one that is an indent and vice versa. If we assume that light is coming from above, if we have a convex object, the shadow would be below it; if it's concave, then the shadow would be at the top, below the rim/edge where light cannot reach. This is a 2D image so we don't have some of our other 3D cues to tell us about the shape of the surfaces here; however, because the image on the left has a shadow on top, we perceive it as concave/indented, while the image on the right, with the shadow on the bottom, is convex/ a bump. Flipping the image changes the position of the shadpw relative to the object and light source and so we perceive the shape differently. This is actually the same principle for how we would apply makeup to, for example, make our cheekbones stand out: you would put something light above the cheekbone and something dark below; this simulates the shadow that a pronounced cheekbone would cause and makes it appear more like a bump.

So what is the "true color" of an object? Color is not a physical property, but a psychological one / a property of the nature of our visual system and how it interacts with light. The physical property of objects that is relevant for this is surface reflectance, which we can describe objectively and independently of the visual system that detects the reflected light. If we had a different visual system, or, as shown above, if we just change the context or our assumptions about the world, objects can appear (i.e. we can experience them) different, but their properties are constant.

There is no exact color of things.

Colors of objects depends on the wavelengths of light emitted by objects and the interpretations of those wavelengths by eyes and brains.

Point 1.

Light wavelengths are real, but colors are interpretations of eyes and brains.

Light comes in a wide range of wavelengths. Human eyes see wavelengths between 400 and 700 nanometers. Bees see light from 200 to 600 nanometers. See the third image on this page.

Different wavelengths of light stimulate cones in the eyes of human and bees. This stimulation is interpreted by the human and bee brains as colors.

Look at the image on this page. The top row is how these flowers look to humans. The bottom row is how the same flowers look in ultraviolet which bees can see.

So which is the "real" color of the flowers? What humans see? Or what bees see?

Point 2.

Your point that the wavelengths of light shone on objects changes the wavelengths of light reflected off objects that reaches our eyes.

Point 3.

As objects get hot, they can emit more than reflected light, and start emitting their own light at different wavelengths depending on how hot they are. This called black body radiation.

Look at image on this page. Near the center of the image is the vertical rainbow showing where the visible light our eyes can see is. At room temperature, 294° kelvin, objects are emitting wavelengths of reflected light that we can see with our eyes.

As objects, e.g., piece of metal, heat up to say 3000° Kelvin, objects glow red because the strongest wavelengths of visible light are at the red end. At 6000° Kelvin, objects glow white because wavelengths of visible light are equal across across all visible light spectrum. At 10000° Kelvin, objects appear blue because the strongest wavelengths of visible light are at that end of the spectrum.

Color is a tricky thing, especially if you involve people's perceptions of color. (For example color blind people see color differently)

Light has a wavelength which is related to color. Separately it has an intensity, which is the amount of that light.

Light can be a whole mixture of different wavelengths all at once. The result is what we call the color of the light. This is often expressed as a graph called a spectrum. On the x-axis is the wavelengths of light, and on the y axis is how much of each wavelength is in the light.

It gets a little bit tricky as a whole bunch of different combinations are seen as the same color by the eye. But they don't have the same mixture of wavelengths, and if sent to a prism will look different.

So that defines the color of the light but not the color of an object. Objects reflect and absorb different wavelengths of light differently.

You can make a graph of how much an object absorbs each color of light as a function of wavelength.

So the color of an object ends up being the color of the light you are looking at it underneath, modified by which wavelengths it absorbs.

We often refer to colors of objects as if viewed under white light, which is a roughly even mixture of most of the wavelengths. So a red object, absorbs most of the wavelengths of light except red ones. And it reflects the red light which is why your eye sees it as red light coming from the object.

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Probably the most important thing to appreciate when thinking about colour and colour perception is that the way the human brain processes what the eyes see is very complex and has a huge influence on how we perceive colour that is distinct from what colours are, in terms of the light entering the eye.

In terms of light, an Individual photon has a frequency that relates to colour: lower frequency for red, higher for blue. Of course there isn’t just one photon, there are loads of them. If the mix of photons come in all frequencies in equal numbers, we call that “white”.

The human eye has three types of sensing cells that relate to colour, one type is most sensitive to lower frequencies, and sees red, one to middle frequencies, and sees green, and one for higher frequencies, and sees blue. They are not, however, narrowly sensitive, so their ranges overlap to some extent. If we get some red and some green, we perceive that as yellow. However, this can happen in two ways. One would be photons of a single frequency between red and yellow, that equally excite the red and green receptors, the other is a mix of red and green separately. The eye can not differentiate between these two cases.

The perception of colour is affected by how the brain handles what you see. The brain is inclined to presume the light around you is white. If the light around you is not white, the brain will adjust how it weights the intensity of the average light it is getting from each of the colour cells to make you think you see white, but the effect of this is the adjustment will alter how you perceive actual colours. If the ambient light is yellow (so less blue than true white), the brain will amplify the blue it gets to compensate, so you perceive the world as being more blue than it really is. This effect can persist for a time. There was a restaurant I used to go to that had pink lighting, and after spending a while there, when I went outside, for several minutes the whole world looked green.

if you have a light source of a certain colour, how you perceive it will depend not only on its colour but also how intense it is relative to all the other light. If it is very bright relative to the ambient light, it will trigger your brain’s white rebalancing, so it will seem more white to you.

Some of these brain perception effects in unusual light conditions can lead to strange illusion effects, a classic example being the photograph of the dress from a few years back that some people see as blue and black, and others as white and gold.

In general, we perceive color based on the wavelengths of light that are reflected off of an object. Different objects reflect different wavelengths of light, which our brain then interprets as different colors.

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One thing to add to the other answers: The color-receptors (cones) and the black/white-receptors (rods) do not have the same sensitivity towards light. The rods are much more sensitive and they are basically what we rely on in the dark. That is why in sufficient darkness there are no colors for you to see. They are there, but your receptors do not see them.

edit: wording