The answer seems obvious: without white balance, we would have bad color reproduction, because different lighting would produce lots of different color tints. Our eyes adjust for the color tints so we can reconstruct the real colors of objects, so cameras need to adjust white balance too.
But that seems strange. We clearly can perceive color tint in scenes: everybody can see that incandescent lamps are yellowish, while fluorescent lamps are very white/slightly blue. But with auto white-balance, the color tint is removed in the photograph. Both incandescent lighting and fluorescent lighting become white.
And though our eyes do adjust to color tint, why don't they adjust when looking at a photograph? Why does the camera need to do work that the eyes would already do?
This seems to imply that to get accurate color reproduction - including color tint that we perceive and thus want to capture, just set the white-balance to daylight, all the time.
But white-balance evidently is necessary. Even in a room with terrible incandescent lights that give off a strongly perceptible yellow cast, the image on the digital viewfinder still looks much more correct with the white-balance on automatic, than with it on sunlight! I just stood there messing with the camera for quite a while, and I'm still really confused why this is the case. Why would the viewfinder in the room, which shows an image without yellow tint, look correct literally right next to objects illuminated with a strong yellow tint? And when I put the camera on sunlight, the screen suddenly shows a WAY stronger yellow tint than the actual room, even though my yellow-adjusted eyes should shift both the room and the screen back to white, no?
Is there something about screens and photographic paper that make our brains/eyes "turn off" our internal white-balance correction?
Answer
The perceived color of an object depends on two elements: the intrinsic color of the object, and the color spectrum of the light shining on it.
A red apple for example, will appear nearly black with a pure blue light shining on it. Depending on the difference in spectral density of different lights, the absolute perceived color of the red apple will change, it isn't constant. But because we have knowledge of what color the apple really is, our brain adjusts our color perception so the red apple is what we expect.
White balance is the tool to make the output of the camera reflect the post-processing our brains do.
When we look at a photograph or a screen, our visual cortex applies its white balance depending on the lights in the room and your knowledge and preconceptions of what the intrinsic colors of items should be, but it's not equipped to make extra, special adjustment knowing it's looking at a photograph. When the white balance of the photo or screen is different than the environment you are in, the resulting colors look strange, e.g. the red apple's perceived color is different than what your brain expects in your rooms lighting.
You say everyone can see that incandescent lamps are yellow, but that's not strictly true. You have knowledge of the lights in comparison to other light sources which is why you think it's yellow, but that can easily be fooled. I could put you in a room, new to you, with only incandescent bulbs, and I could make the lights seem virtually any color, by carefully selecting the colors of the paint and other objects to trick your visual cortex into applying an incorrect white balance. If I had a bunch of objects in the room that are ordinarily white, but are in fact tinted a particular way, your brain will adjust its white balance correction so they are, and that can result in perceiving the incandescent lights a different color. The infamous blue/gold dress is an example of the phenomenon at work.
The Wiki page on Color Constancy has more explanation as well as some sample images that can further illustrate the concept.
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