I took a class in 1976 about perception and psychology. It dealt with colors and light. Here is what I recall that is related to this subject.
There are two basic light concepts--direct light and reflective light. (not the terms they used but best for my explanation). Direct light is produced from the source, ie a light buld, sun, etc. while reflective light is produced from the reflection off an object. For example, in sunlight, if you see a red ball, you see it as red because it absorbs all of the colors of light except red. Red is reflected from the ball and hence you have a red ball.
We perceive sunlight as white. White light is made up of all the colors. A rainbow is a good example of refracted direct light ie white light being split apart into its different colors. As I recall red bends less than blues. Red also has a greater wavelenght than blue. The bending less explains why our sunsets are red and not blue. White light as it aproaches the earth is affected by gravity and the blues tend to bend more toward earth while the reds travel a longer distance. Thus, when the sun is low, only reds reach us on the edge of the planet.
In water, white light enters and the reds, being the larger wave length, are filtered out leaving only blue (small wavelength light) to pierce into the depths.
Your eye is designed around white light--sunlight. At depths, you see a blue tint because your "white light designed" eye is seeing things illuminated by blue light. Now, if you notice, you see some yellows, reds, etc. even in deep water. This is because those things are absorbing blue light to make use of it and reflecting red light which they have no use for.
Take a digital camera, it is designed to see white light, just like we are. When you go deep, it sees the same blue light you and I see thus the photos are blue. If you change the white balance, you are telling the camera that it is looking at blue light instead of white. Then, when it sees red light reflected from an object it "says," "if I saw this object in white light, it would be red. So, since I'm in blue light I have to adjust the way that I absorb light so that the reds come out red." Not knowing a lot about how digital works, I'll bet it simply makes a new calculation for the colors it is "seeing." That is why you have white balance, you show your camera white at 40' and it adjusts its calculations accordingly. At thirty feet, there is more red and if not re-white balanced, it makes the same calculation as at 40' and mistakenly gives everything a red tint.
Film cameras don't make calculations. They take the light in the area and expose the film to it and the film burns it as it sees fit. That is why there are different films that will emphasize blues, reds, etc. If you look at slide film, its colors are much more vivid. I think that is because it is designed to bring out the blues and greens more, it burns slower, and it is less grainy. Therefore, you will get different results with the same settings and different film at 40'.
Filters prevent colors from flowing through. The red filter reduces the amount of blue light that comes through and, at the correct depth for that filter, will "balance" out the reds and blues to look more like white light on the surface. My guess is that darker red filters are better in deeper waters. Filters effectively subtract colors from light. In film cameras, this means at 40' less blue light is hitting the film than if there were no filter. The result is that the film looks more like it was exposed to white, not blue, light.
A flash brings "white" light to the depths and provides an effect similar to white balancing but it supplies additional brightness at depths. The brightness sometimes helps the picture look better.
Now, having said all this, it has been a number of years since I studied it so those of you who can explain it better, please do so.
rodney