Page "Diffraction grating" Paragraph 8

An idealised grating is considered here which is made up of a set of slits of spacing d, that must be wider than the wavelength of interest to cause diffraction.

When a plane wave of wavelength λ with normal incidence, ( perpendicular to the grating ) each slit in the grating acts as a quasi point-source from which light propagates in all directions ( although this is typically limited to a hemisphere ).

After light interacts with the grating, the diffracted light is composed of the sum of interfering wave components emanating from each slit in the grating.

At any given point in space through which diffracted light may pass, the path length to each slit in the grating will vary.

Since the path length varies, generally, so will the phases of the waves at that point from each of the slits, and thus will add or subtract from one another to create peaks and valleys, through the phenomenon of additive and destructive interference.

When the path difference between the light from adjacent slits is equal to half the wavelength, λ / 2, the waves will all be out of phase, and thus will cancel each other to create points of minimum intensity.

Similarly, when the path difference is λ, the phases will add together and maxima will occur.

The maxima occur at angles θ < sub > m </ sub >, which satisfy the relationship dsinθ < sub > m </ sub >/ λ =| m | where θ < sub > m </ sub > is the angle between the diffracted ray and the grating's normal vector, and d is the distance from the center of one slit to the center of the adjacent slit, and m is an integer representing the propagation-mode of interest.