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A grating sends light of wavelength lambda to angles where d sin(theta) = m.lambda. A 600 line/mm grating has d = 1.667 microns, so 550 nm light appears at 19.25 degrees in first order. Higher orders sit at larger angles until sin(theta) would exceed one, which caps the observable orders at three here.
Grating equation
d sin(theta) = m lambda
Grating spacing
d = 1 / lines per metre
Because dispersion is far larger and is calculable from geometry alone, and higher orders can be used to multiply resolution.
The requirement that sin(theta) stays under one, so m cannot exceed d/lambda. Coarse gratings show many orders, fine ones only a few.