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Why is white light separated into a spectrum of colors when it is passed through a diffraction grating?

The diffraction angle (theta) is given by

n x (lambda) = d sine(theta)

lambda = wavelength
theta = diffraction angle
d = grating spacing
n = order (1,2,3 etc.)

so each wavelength is diffracted through a slightly different angle. If the incident light is white light then you will see a rainbow at each value of n.

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