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When the two additive colors blue (475 nm) and green (510 nm) are incident in equal magnitudes upon a white screen, the subtractive color cyan results. Consider two beams, one blue and one green. The blue beam is shined through a double-slit diffraction grating with slit distance of 0.0400 mm and then displays an interference pattern on a screen 1.00m 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?
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Let's put the facts clearly. Blue wavelength lam*b = 475 nm, cyan wavelength = 510 nm, green wavelength lam*g 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(m*lam/d) (see img.)
Thus lam*g/dg = lam*b/db
==> dg = db*lam*g/(lam*b)
= 0.04 mm*540/475

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