Diffraction Grating Calculator (Angles of the Orders and Spot Positions)

What this tool does

A grating with N lines per millimetre has a line spacing d = 1 ÷ N, and light of wavelength λ reinforces at angles where d sin θ = mλ, one for each whole number m, the order. Since sin θ cannot exceed 1, only orders with mλ < d exist, which is why a coarse grating gives many orders and a fine one only a few. The angle grows with wavelength, so a grating spreads white light into spectra, red furthest out, the reverse of a prism, which bends blue the most. A common classroom use is to find an unknown wavelength, such as that of a laser, from the position of the spots.

Formula

d sin θ = m λ · d = 1 mm ÷ lines per mm · highest order < d ÷ λ · dθ/dλ = m ÷ (d cos θ)

Variables

Worked example

Limitations

• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
• The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.