Diffraction Grating Calculator
d sin θ = mλ, with the orders that actually fit.
Work out Diffraction Grating. d sin θ = mλ, with the orders that actually fit. Names the assumption that breaks it.
1 is the first bright fringe either side of the centre.
Diffraction angle, order 1
17.458°
3 orders available · slit spacing 1,666.7 nm
d sin θ = mλ. Because the angle depends on wavelength, a grating spreads light into a spectrum — and it separates colours far more sharply than a prism does, which is why spectrometers use gratings rather than glass. Only a finite number of orders exist, since sin θ cannot exceed 1. A finer grating spreads the spectrum more but fits fewer orders, which is the basic trade-off in choosing one.
How the Diffraction Grating Calculator works
Enter lines per millimetre, wavelength and order for the diffraction angle, along with how many orders exist at all. Orders beyond the maximum are refused rather than returned as an error value.
Also known as: grating equation calculator · diffraction angle calculator · d sin theta = m lambda · spectrometer grating calculator
Frequently asked questions
What is the grating equation?
d sin θ = mλ, where d is the slit spacing, m the order and λ the wavelength. Slit spacing is the reciprocal of lines per unit length.
Why do gratings beat prisms in spectrometers?
They disperse light far more sharply and the relationship between angle and wavelength is simple and linear in sin θ. A prism's dispersion depends on the glass and is strongly non-linear.
Why do only some orders exist?
Because sin θ cannot exceed 1. Once mλ passes d there is no angle that satisfies the equation, so that order simply does not appear.
Does a finer grating always work better?
Not always. More lines per millimetre spreads the spectrum further, which helps resolution, but it also reduces how many orders fit and can push the useful ones to awkward angles.
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