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light interference help?
when the two additive colors blue and green are incident in equal magnitude upon a white screen, the subtractive color cyan results ( 475 nm and 510 nm respectively). consider two beams, one blue and one green. the blue beam is shined through a double slit diffraction grating with slit distance of .0400 mm and then displays an interference pattern on a Screen 1. m away. if the green beam is then shined from the same position as the blue beam ,what size diffraction grating would be required for the green beam so only a cyan interference pattern would be seen on the screen?
Let's put the facts clearly. Blue wavelength λb = 475 nm, cyan wavelength = 510 nm, green wavelength λg is longer than cyan (~540 nm). In the final situation, blue, green and cyan are present, but blue and green pass through different slit separations (db and dg). How do we have both the blue and the green off-screen without losing the cyan?
We must suppose that whatever deflection (theta) the blue beam undergoes puts it off-screen, since we can only adjust the green beam. Then the green beam should have dg adjusted for the same theta as the blue beam.
Theta = arcsin(mλ/d) (see ref.).
Thus λg/dg = λb/db ==> dg = db*λg/λb = 0.04 mm*540/475.
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