Diffraction Grating Calculator

Grating Spacing is the physical distance between adjacent slits, which is simply 1 divided by the number of lines per millimeter -- so packing more lines into the same millimeter necessarily squeezes them closer together. A 1200 lines/mm grating has half the spacing of a 600 lines/mm grating.

It means the diffraction grating equation d sin(θ) = mλ has no valid angle for the order and wavelength you entered, because mλ/d would need to exceed 1 -- and sine can never exceed 1. Physically, that diffraction order simply does not exist for this grating and wavelength; try a lower order, a coarser grating (fewer lines/mm), or a shorter wavelength.

A finer grating (more lines per millimeter) has a smaller Grating Spacing, and Max Observable Order is roughly Grating Spacing divided by Wavelength -- so a smaller spacing directly caps how many diffraction orders can satisfy the equation before sin(θ) would need to exceed 1. This is a real physical trade-off: finer gratings spread light out more per order but support fewer total orders.

Yes eventually, holding the grating fixed -- though because the order count is a whole number, small wavelength changes often leave it unchanged before it drops by one. Max Observable Order is Grating Spacing divided by Wavelength, so a longer wavelength (redder light) divides into the same spacing more coarsely and reaches the sin(θ) = 1 limit at a lower order number than a shorter wavelength (bluer light) would.

Angular Dispersion measures how many degrees the diffraction angle shifts per nanometre of wavelength at the order you selected -- it's the property that makes gratings useful in spectrometers, since a higher dispersion spreads different wavelengths of light into more widely separated angles, making it easier to resolve closely spaced spectral lines.