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I am concerned about the accuracy of some information in a science textbook which I would like to clarify please. When white light is shone through a blue filter, only blue light will pass through. When the emergent blue light is passed through a red filter, no light gets through, because there is no blue light left. This makes perfect sense. However, what would you expect to see, and why, if white light is shone through:

  1. a yellow filter, followed by a blue filter?
  2. a blue filter followed by a yellow filter?
  3. a yellow filter followed by a red filter?
  4. a red filter followed by a green filter?
  5. a green filter followed by a yellow filter?
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2 Answers 2

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The results will depend on the filter transmission bandwidth. For near-ideal filters with short bandwidth (transmitting only one color and absorbing/reflecting others), virtually no light will be transmitted in any of these cases. The order of the two filters doesn't matter.

When using wide band filters, some light between the peak transmission wavelengths (colors) of the filters might pass through. Usually, the farther apart the wavelengths, the dimmer the transmitted light: this is why you see little to no transmission using blue and red filters. The perceived color will likely correspond to a wavelength somewhere between the peak transmission wavelengths of the filters. Refer to the visible spectrum below. The transmitted light will likely appear green for blue and yellow filters, yellow for green and red filters, etc.

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My guess is that the author of the textbook has the common misconception that there are only three colors—red, green, and blue—and yellow is red+green. Therefore, you're expected to answer that the red+yellow filters will let through red light, and the green+yellow filters will let through green light, and the others will let through nothing.

That isn't actually true. Light comes in a continuous range of wavelengths; filters can in principle block any of those wavelengths and let any others through; and there are many different combinations of wavelengths that we'll perceive as red, yellow, green, or blue.

On this page I found a chart of the transmission spectra of some color filters:

These aren't canonical transmission spectra of filters of those colors; they're just examples of particular filters made by one company. There's no yellow filter on the chart, but you can probably imagine that it's similar to the orange filter, but shifted farther to the left.

You can see that even the red and blue filters together will transmit some light, in the 600-700nm range, which will probably look red or a bit orangish. It will be dim, though. The green and blue filters together will transmit a larger amount, which may appear blue-green in color. And so on. Again, these are just examples; you can't be sure how any two filters will appear in combination unless you know their transmission spectra and the spectrum of the light you're filtering.

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