# What is diffraction grating

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

A diffraction grating is formed by an evenly spaced series of lines, slits, or other periodic array of reflective or transmissive elements. It is typically used for analyzing the spectrum or measuring the wavelength of electromagnetic waves, particularly in or near the visible part of the spectrum.

Equations

For a normally incident wave, waves are diffracted at angles such that

$$d\ \sin \theta_m = m\ \lambda$$

where m is any integer.

For other angles of incidence, the diffraction condition is

$$d\ ( \sin \theta_m - \sin \theta_i ) = m\ \lambda$$

For nonzero m, a requirement for diffraction is

$$d > \lambda$$

Extended explanation

Definitions of terms
θm = diffracted angle of mth-order wave
θi = incident angle of wave
m = (any integer) order of the diffracted wave
λ = wavelength
d = line spacing, or period of diffractive elements​

Note: it is common practice to specify the number of lines per mm, cm, or m for a diffraction grating. This is simply the reciprocal of d; eg. a 1000 lines/mm grating has d=0.001mm

Reflection and transmission

A diffraction grating may work either in reflection or transmission, as shown here:

* This entry is from our old Library feature, and was originally created by Redbelly98.

Last edited by a moderator: Jul 27, 2014