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I found in this site that if we use a set of colored lights we'll have colored shadows. But why is that?

As far as I know a shadow is where there is no light. So why isn't the shadow that is produced by colored lights just black like a normal shadow that is produced by white light?

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With just a single colored light, you'll find that colored light does indeed produce a "black" shadow (the absence of light), just like your intuition suggests.

However, in the linked example, they don't just have one light, they have three of different colors. In that case, in the shadow from one light you still have two colored lights lighting up the background. Those two colored lights mix to yield the "colored shadow" that you perceive.

The paradox would feel less strange if your mind recognized white as "all colors." In that case, you'd comfortably see that there's simply one color missing in the shadow. However human perception of color doesn't quite work that way. We typically think of white as "not colored" so its a bit of a surprise to see color appear in the shadows. When you consider how light actually adds to produce colors, the result is less surprising.

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If you have only one color shining on you the shadow is black. In the experiment shown in your link you have different colored lamps, at different spots so if without shadow the wall is almost white, so if you take away the red light you see in the "shadow" white minus red wich is greenish and so on , in the picture with the hand you have all three shadows, black where no light reaches the wall , green wehre no red, and red where no green.

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