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The shortest answer to your question is: physics and chemistry!

Ok so just a couple quick things: you are correct that the color we perceive is based on the spectrum of light which reaches our eyes. But there are a lot of other factors beyond the pure absorption of the object. For example, the spectrum of the source (eg a lightbulb has a different “color” of light than the sun) as well as the intervening medium (air interacts with light differently than glass, and dusty air is different than pure air). And there are ways for light to interact with an material beyond absorption (like scattering). But generally speaking you’re on the right track.

So, light comes in discrete packets called photons which have an energy. Because of quantum mechanics that energy is directly linked to the wavelength. In other words, different wavelengths of light have different energies. When light hits an object, light is so tiny that what we’re really talking about is light hitting the molecules which make up that object. Now, again due to quantum mechanics, each molecule (and each part of the molecule) can only have different set energy states. Making up numbers but let’s say it can be 1, 2, or 2.5. But it can’t be say, 1.7 or 2.8. So going back to the light, let’s say the molecule is generally in state 1, which physicists call the ground state. If the photon has an energy of 0.7 it can’t interact* with the molecule, but if it’s 1 it can boost the molecule up to 2 and if it’s 1.5 it can boost the molecule to 2.5. Now, remember that each energy of photon is tied to a wavelength? This is the mechanism by which some wavelengths get absorbed but others do not. For a given material this is expressed as an absorption spectrum, which is a graph that shows how strongly different wavelengths of light are absorbed. Add together a weighted average of the absorption spectra for all the materials in the skin of an apple, and you get the overall absorption spectra which determines what color the apple’s skin is. In the case of a red apple, shorter (bluer) wavelengths are more strongly absorbed than longer (redder) wavelengths.

As to where that extra energy goes, the molecule will eventually return to its ground state. In most situations for light in the visible spectrum, the energy ends up lost to heat (at a molecular level, the molecule wiggles a bit faster). In other words if you shine a light on a thing, it’ll get hot over time and that heat is the energy coming from absorbed photons.

Now, I’m glossing over a whole lot here, and the reality is more complicated than I’m describing in a lot of important ways. For example most molecules have tons and tons of different energy states, eg vibrational, rotational, electron energy levels, chemical bonds, etc. And in practice there’s usually a narrow range of acceptable energies that mean you don’t get a perfectly sharp peak. But hopefully this is enough to get you started.

>what we mean is apart from all the visible light from the spectrum, red wavelength is reflected back to our eyes and rest all is absorbed

Actually, no. The perception of red is based on a weighted average of reflectivity at three different wavelengths. https://sciencedemonstrations.fas.harvard.edu/presentations/lands-retinex-theory-experiment#:~:text=What%20It%20Shows See also https://commons.trincoll.edu/wmace/courses/perception/lands-retinex-theory/#:~:text=The%20term%2C%20%E2%80%9Cretinex%E2%80%9D%20was%20coined%20by%20Land%20to,this%20by%20combining%20the%20word%20%E2%80%9Cretina%E2%80%9D%20with%20%E2%80%9Ccortex.%E2%80%9D

So your other question has to be rephrased a bit: what decides at the very root level, which wavelength_S_ to be absorbed _to what extent_ and which _oneS ARE_ is to be reflected _to what extent_. Very few things in the natural world reflect just one wavelength, nor even just one narrow range. For most things in the natural world, there's a mix of reflectances (and there can be other effects, as on butterfly wings).

Thanks for sharing the link.

Thanks for explaining.

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The keyword for this is "chromaphore", if you want to dig deeper. This will take you to molecular orbital theory, that is the description of the energetic states of electrons in molecules.

That's a great explanation of the absorption but I think the other missing piece of the puzzle is why the photons that aren't absorbed must be scattered or reflected instead of passing straight through (after all, atoms and molecules are mostly empty space). We know visible light can pass through some solid matter and radio and microwaves can pass through apples.

I don't relish pointing that out because I know the answer isn't easy: I think an answer to that might be need to get into the realms of QED and particle interractions. Nevertheless, I do think any answer to why an orange is orange (not all apples are red so not a great example imo) needs to explain why orange is scattered or reflected and not just why non-orange light is absorbed.

I would add an interesting chemistry tidbit that has to do with colors.

Different chemical bonds will absorb different wavelengths of electromagnetic energy depending on how stable they are. In organic chemistry, a lot of times that has to do with how much electrons are delocalized (or “have the freedom to move to different bond sites”) over large numbers of double bonds. If you look up the structure for carotene (the chemical that makes carrots orange), you’ll notice a ton of these alternating single and double bonds. The electronics are delocalized over that whole stretch. That pushes the absorbance to higher wavelength. A lot of molecules of colors have a high degree of stabilizing electron resonance like that. Tomatoes have even more conjugation so they absorb higher up into the red wavelength region. In general, all those are high wavelengths for chemical bonds to be absorbing, which is why it takes so much conjugation. More typical bonds with less conjugation will absorb down in the UV spectra or lower wavelengths.

Here’s a source that talks about some colors in food and their chemical structure. Oh it has blueberries too! That molecule looks super cool. :)

So far, I did understood things, these are all under natural circumstances. So, taking apple example forward what if I project green or blue light on it? It won't be showing red colour then. Or atleast not the same way. Now that incident light has changed so the internal molecules or atomic system like electrons jumping form one state to other..etc will also change depending upon the energy it gets and time it takes to dissipate. All the physics I get it but it is too limited I think. Because it is with respect to ours.

Now do the same experiment with animals, their perception of colours is vastly different. So, for them also things are happening the same way like for us, but it is possible that they perceive and their perception of colours are much stronger or weaker than us. Or take people who are colour blind.

What I'm confused about is why are some absorption spectra shown as graphs with a continuous line? I was under the impression that only specific light with one or more specific energy, frequency, and wavelength could be absorbed by a given atom/molecule. Also, how do we find what color something appears to be from it's maximum absorption? For example, water absorbs red more than other visible light, so it's absorption maximum that we can see is red. How do we know from this that water is blue? I know there are complementary colors but I'm confused on how we actually got those. I made a post here recently asking basically this but it hasn't been put up yet.

Like I said in my final paragraph, I was glossing over a lot :P

So any given molecule has a lot of energy levels. And for each of those transitions, there is actually a narrow range of acceptable wavelengths that will be absorbed. Start adding all of those together and what you end up with is that pretty much any wavelength of light can be absorbed, some are just much more strongly absorbed than others.

So an absorption spectrum is showing how strongly light is absorbed. The higher on the y axis, the more of that light gets absorbed by the material and the less is available to reach your eye.

Looking at water, it strongly absorbs UV (high energy light) and then there is a big drop and it has a minima right around 420 nm, which is blue. From there are the wavelength gets longer (redder) the graph ticks back up until it passes into the IR. So this tells us that water passes blue light and absorbs red light. So if you shine a red light through water, it will go away much faster than if you shine a blue light. From the graph we can (successfully) guess that water will appear blue or blue-green because it more easily allows blue light to pass (and reach our eyes) than it does yellow/orange/red light.

Complementary colors have more to do with how we perceive color than with how light works. It’s about which colors look good together rather than how those colors are made.

Thank you for elaborating! So the color of something is mainly based on what color of those that we can see that is absorbed least, pretty intuitive. I'm assuming there are also times when we would have to take combinations into account if there are a few wavelengths that are not absorbed much? Also I was reading a bit more about complementary colors and I think the premise is that 2 complementary colors would combine to form white. So I guess the idea is that if one color is absorbed much more than others, we would interpret the remaining light as the complementary color to the one that was absorbed, since the light was initially white and lost a lot of light of a specific color.

And 1 more question, does an emission spectrum for some molecule give essentially the same information as an absorption spectrum?

Key distinction: the color of something is based on the spectrum of light (how much light at each wavelength in the visible range) reaches our eye. Absorption is a big part in that, but it’s not all of it. For example: an apple won’t appear red if the light illuminating it doesn’t include any red light since there’s no red light there to reach our eyes. And there are plenty of situations where optical effects other than absorption are dominant. A great practical example is the Lycurgus Cup. It’s a glass cup full of gold nano particles. When light shines through it, absorption dominates and so only red light passes through and it appears red. When light shines on it, scattering dominates, and those same particles scatter green light, but not red or blue, so it appears green since the scattered green light is reaching our eye.

Also, up until now we’ve been talking about the light itself. How we perceive that light and turn it into our sense of color is a whole other part of this. Very simplified explanation but: our eyes contain two types of light sensitive cells, rods and cones. Rods are great in low light conditions but can only see black and white. Cones are less sensitive to light, but they come in three variants, red, blue, and green. Red cones most strongly absorb red light, blue cones most strongly absorb blue and green absorbs green. When a cone absorbs light, it sends a signal to our brain. Based on how many of the RGB cones are triggered our brain mixes those signals together to form a perceived color. So complimentary colors have to do with how our eye and brain perceive colors. I don’t think there’s anything inherent to the photons that makes, say, blue the complement of red. It’s the way our sense of color works that makes those have high contrast.

Emission specta (or scattering spectra, or transmission spectra, etc) are basically the same yeah. You read the wavelength (or frequency) of light along the x axis and the y value tells you how much is emitted/scattered etc for that wavelength. It’s been a while but I think for an emission spectrum you need to specify the conditions under which the object is emitting.

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> In other words, different wavelengths of light have different energies.

Is that only because shorter wavelengths lead to more oscillations per time, thus more kinetic energy in the affected charge? Or is there another reason for higher frequency light containing more energy?

How do you shine light on something vs through something? And I agree that the whole complementary color thing doesn't tell us much about the light inherently but it still seems useful (or at least interesting) to determine what color we perceive things to be.

Ok, it’s been a while since it took physics so if I’m wrong someone can correct me:

No, moving charge doesn’t have kinetic energy because it has no mass. The link between photon frequency and energy is called the Planck Relation.

Basically is it backlit or lit from the front. If you backlight the cup you are looking at the light that has passed from the light source through the cup and then reaches your eyes. If you put the light on the same side of the cup as you, then you are looking at light which hits the cup, reflects or scatters off the glass and gold and then reaches your eyes.

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> No, moving charge doesn’t have kinetic energy because it has no mass.

I dont think there is a charge that has no mass. Light is not considered having a charge, protons and electrons are, and those have mass. Maybe I should have said 'charged particle' but it should be synonymous. Your link unfortunately does not answer the question.

Sorry, brain fart above and I typed the wrong thing: I means that a photon does not have kinetic energy because a photon has no mass.

Hopefully someone with more knowledge can jump in, but I don’t know that there’s an intuitive reason why Planck’s Relation is true. I think it’s a relationship derived from the Schrödinger Equation and Einstein’s work on relativity and then extensively measured and confirmed since then.