under what circumstances red shadow can be formed

A SHADOW CAN BE FAINTLY FORMED BY A TRANSLUCENT MATERIAL AND SO IF THE MATERIAL IS RED, THE SHADOW CAN SLIGHTLY SHOW THE SIGNS OF RED IN IT. FOR EXAMPLE, IF YOU CAREFULLY LOOK AT THE SHADOW OF A PAINTED RED GLASS, YOU CAN SEE THE SHADOW AND THE RED IN IT FAINTLY.

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Shadow is always black.
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The red sheet absorb all other colours of white light only allowing red light to pass through it.
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If the material is painted red, shadow can show some signs of red color
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If you pass white light through a red filter, then red light comes out the other side. This is because the red filter only allows red light through. The other colours (wavelengths) of the spectrum are absorbed. Similarly, a green filter only allows green light through.
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