The "illusion" is that C looks darker than B, when in fact they are the same value:
This is instructive because it demonstrates both the malleability of mid-tones (a single tone can appear as light or shadow) and our inability to accurately gauge them, even in relative terms (which is, in fact, saying the same thing). We have no difficulty identifying the darkest and lightest values in the picture, but when it comes to ranking the "two" in the middle we have trouble - we can't even tell that they're two different values. As a side note, it also shows that as creatures trying to survive, it's more important for us to know that B is a white square and C is a dark square - so we filter out the shadow effect and see B as lighter than C.
The other illusion here is that we perceive this simple arrangement of three values as something else - a checkerboard with a shadowed area, or perhaps an area with some dark translucent material over it (there is a very close relationship between the illusion of light and the illusion of transparency). As representational artists our goal is to be able to create that illusion at will.
This perception of light and shadow occurs (in the real world as well as in this picture) from a form of pattern recognition. We perceive a consistent checkerboard pattern passing under a consistent darker because the relationship between the white square in light and in shadow (A to B) is the same as the black square in light and shadow (C to D) and the relationship between the white square in light and the black square in light (A to C) is the same as the white square in shadow and the black square in shadow (B to D).
A:B = C:D and A:C = B:D(this is cumbersome to say in words, but easy to see)
If you think about it you'll realize that if the first statement is true then the second one must also be true, and vice versa. If the relationship between A and B is the same as between C and D, then A to C will also be the same as B to D. However, in practice its easier to spot inconsistency by checking it both ways.
It is this set of relationships, fitting together like a value puzzle, that makes the illusion of light/transparency appear. This is what makes us see a pattern of light and shade, and also patterns of light and dark objects, from a simple arrangement of value shapes. It is not the fact that B and C are the same value.
B and C don't have to be the same values:
darker shadowHere I've made the shadow darker, like turning down the ambient light. I've made B and D darker, but the value structure outlined above (A is to B, etc...) is still valid. B and C are no longer the same, though.
Whiter white squares, blacker black squares
Here's another example where B and C are not the same value:
whiter white squares, blacker black squares
I've made the "white" squares appear much lighter, and the black squares much darker, by changing all four values. But still the structure (A is to B... etc.) is intact.
Mid-tones are special
The lightest value must necessarily represent the lightest object in full illumination, and the darkest value always has to represent the darkest object in shadow (we're excluding highlights and fully occluded areas here). By definition, anything lighter than the white's shadow must be an illuminated area, and anything darker than the black's lit area must be shadow. But every value in between, that is, the mid-range values, can be either an illuminated area or a shadow area. Darker mid-tones can be both the lit parts of dark objects and the shaded parts of mid-toned objects, while lighter mid-tones can be both the shaded part of light objects and the lit part of mid-toned objects. Put another way the closer a value is to either end of the range the more limited its role. That is the magic of mid-tones that, if understood, while make your values (and therefore your colors) pump out light!
This is why it is so important to apply mid-tones skillfully when seeking to create the illusion of light. This is also why the illusion of light does not come from simply increasing contrast, or lightening the picture overall.
Turning up the lights too high
Intuitively it seems like turning up the light in the lit areas will create a stronger sense of light. The problem, though, is the lightest color can become pinned against the maximum whiteness of the medium, and so the lit areas of the black squares move too close to them, and the structure (A is to B, etc.) breakes down. Turning up the lights does not increase the illusion of light if the value structure breaks down - and turning them up too high will cause the structure to break down!!
too much "light" = less light
The only difference between this example and the first illustration introducing the post is that the lit area of the black square is too light, which is, paradoxically, breaking down the illusion of light / transparency. The supposedly shaded rectangle is starting to split off from the checkerboard. We sort of don't know what to make of it. It looks like there's a haze over the lit parts, and then a hole in that haze for the shaded rectangle, or something. It's ambiguous - and there goes your illusion of light!
What's really interesting here, and even more stunning when you encounter this problem in a real panting is that to fix this image, to add more light we make a lit area darker. This isn't darkening an area to make another look lighter by contrast it's darkening a lit area to make it appear to have more light. This is a very practical situation that occurs in a lot of paintings. Don't fall into the trap of thinking lighter lit areas = more light.
The wrong way to increase contrast
In the "darker shadow" example above we made the shadow area darker while preserving the basic value relationships. If we make it too dark, what happens is the shaded black squares (D) become pinned (they can't go any darker) but the shaded white squares (C) continue to get darker, and hence become relatively closer to D, breaking down the basic structure.
muddy shadows = less light
Another way to describe this is that cutting off the low (or high) end of the value structure is actually fine, in terms of where the ends are - the problem is this changes the relationship of the middle to the ends.
Overall lightness or "high key"
Sometimes we think making the painting lighter overall will create the illusion of light. It's fine to make paintings light overall, but that alone does not increase or make more likely the illusion of light. In fact, in practical terms, by reducing your available range of values the job of structuring them properly demands more precision. Here is a high key image with broken value structure:
high key misfire
The picture is lighter overall, but the value structure has broken down because the shaded area of the white squares is too light, creating an ambiguous situation. Here's it is adjusted properly:
high key with working value structure
With overall lighter values you need to be a lot more precise in value management, because the range you're working with is smaller (which is fine of course, if that's what you want to do). So the high key picture is working, but is the illusion of light weaker or stronger than in "whiter white squares, blacker black squares," above? I think the "whiter white squares..." is stronger because it's using a wider value range (still a tiny fraction of the real world). Of course there are many other reasons to restrict your image to only light values or "high key."
We can even make the entire image very dark, while still preserving the illusion of light better than in the high contrast, but imbalanced examples:
dark image with working value structure
Ultimately you really need to learn to just see these relationships - but often we don't know what we're looking for. Our inability to accurately rank middle values is not a failure or shortcoming of our visual system. In painting, as in perceiving reality, we don't need to be able to tell what something is in terms of its value - just what it looks like it is. This is a gift - use it!
Look at a given object in your painting (or area of local color, such as the white squares in these examples) and see if it seems to be the same color as it pass into the shadow. Do this with all color areas. Then do it with shadow and light areas, like a cross-reference - see if the shadow seems to be equally dark as it passes over all the different local colors and see if the lit areas appear to be equally lit. If all those tests are successful, you'll have the illusion of light.
One easy way to get started is to establish the white object and the black object in your painting, and then in each sub area of the painting. Later we'll see how we might arrive at a solid value structure in a typical painting.