The wave front of the incident light that falls on a diffraction grating is split into several coherent beams by its grooves. The coherent beams, diffracted by each groove, interfere and form the resulting spatial intensity distribution of light. The intensity distribution is proportional to the product of two terms, the interference function and the intensity function of a single slit The interference function is determined by the interference of coherent beams coming from grating grooves. The slit intensity function is related to the light diffracted from one groove.
Two coherent parallel rays, diffracted on one groove spacing of the grating, have the difference in their path lengths or else , where is the angle of incidence, is the angle of diffraction. The corresponding phase difference is The function of – is a periodical one with different intensive principal maxima. The positions of principal maxima correspond to . It can be rewritten as , where is the diffraction order. Eq. (2) can be used to replace in Eq. (1): . Combining this result and Eq. (3) gives , substituting into Eq. (1) gives: Eq. (4) is called the grating equation. It shows that the principal maxima occur at angles which are represented by non-zero integers .
Between the adjacent principal maxima secondary maxima are located whose intensity decreases in proportion to , and minima, where the intensity is zero. The grating equation for monochromators can be written in a more convenient form. The difference between and at any grating rotation is constant. This value is equal to , and it is determined by monochromator optical design.
Here we have defined and , where is the scan angle which is measured from the grating normal to the bisector of the beams, is the deviation angle between the incident and diffraction directions. Thereafter, the grating equation may be simply expressed as: , or otherwise:
A lens can be used to collect the diffracted light coming from the grating, and to form spectra for each value of in its focal plane. For (zeroth-order maximum), the spectrum is not formed, because for all wavelengths. In addition, the zero-order maximum direction corresponds to the specular reflection, i.e. .