What is diffraction grating and how does it work?

[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

θ_m = diffracted angle of m^th-order wave​

θ_i = 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=0.001mmReflection 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.

 

[Wrichik Basu]

A concise post explaining diffraction grating. Thanks @Redbelly98 for writing this.