How this calculator works
A grating reinforces directions where the path difference between neighbouring grooves is an integer number of wavelengths. This page uses the signed-angle convention mλ = d(sinα + sinβ); normal incidence gives sinβ = mλ/d. Density is the reciprocal groove spacing, with unit conversion handled before calculation. It predicts order locations rather than efficiency, which depends on groove shape and polarization.
Formula
mλ = d(sinα + sinβ); d = 1/g. β = asin(mλg - sinα). An order propagates only when the inverse-sine argument lies between -1 and +1.
Worked example
At normal incidence, 500 nm light and 1000 lines/mm produce a first order at 30 degrees. The second order is at 90 degrees and higher positive orders cannot propagate.
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Frequently asked questions
Why is an order unavailable?
Its required sine is outside the real-angle interval.
Can I use negative orders?
Yes in inverse modes. Preserve the stated signed-angle convention.
Is groove density the same as spacing?
No. Density is the reciprocal of spacing; 1000 lines/mm means a spacing of 0.001 mm.