Simple Optics Q: Green Filter + Blue Light = ??

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There was a question on my exam. There is a green filter and blue light is directed to the filter. Normally It should pass through the blue light but my teacher says that we wouldn't be able to see it so the color we see would be black but I think it would be blue. What is the answer?
 
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Usually, when people talks about [color] filter, such as green filter, then they mean a filter which visually appears [color]. So in your case, green filter should appear green. This means this filter only let through frequencies corresponding to green colors and block other frequencies.colors.
 
For an ideal green filter, with just a narrow band pass, the blue light will no go through.
For a real, usual filter (like the ones used in photography), some of the blue will go through.
 
This is not as straightforward as it seems at first. When you buy a filter, specified as green, it will pass a range of wavelengths in the region of 'spectral' green. It's pass band will be quite wide in order that the light coming through will be bright. Your eyes will see about 1/3 of white sunlight through the filter. (If it let only a narrow band it would look very dim)
Blue wavelengths would probably lie outside the pass band so they wouldn't get through.
 
Here's an added confusion which may explain the OP's dilemma. Mixing blue and yellow paint (pigments) will produce a pigment that looks green. If you make a filter this way, it will look green when white light passes through. Blue light will be blocked by the yellow pigment, even though the blue pigment will pass it. The shape of the spectral response of this mixture will probably be very 'sloppy' and might pass a bit of blue but not much. Look up Subtractive Colour Mixing.