When m = 0, the grating acts as a mirror, and the wavelengths are not separated ( β = – α for all λ) this is called specular reflection or simply the zero order.Ī special but common case is that in which the light is diffracted back toward the direction from which it came (i.e., α = β ) this is called the Littrow configuration, for which the grating equation becomes In a given spectral order m, the different wavelengths of polychromatic wavefronts incident at angle α are separated in angle: In geometries for which ε ≠ 0, the diffracted spectra lie on a cone rather than in a plane, so such cases are termed conical diffraction.įor a grating of groove spacing d, there is a purely mathematical relationship between the wavelength and the angles of incidence and diffraction. If the incident light lies in this plane, ε = 0 and Eq. Here ε is the angle between the incident light path and the plane perpendicular to the grooves at the grating center (the plane of the page in Figure 2-2). If the incident light beam is not perpendicular to the grooves, though, the grating equation must be modified: Most grating systems fall within this category, which is called classical (or in-plane) diffraction. (2-2) are the common forms of the grating equation, but their validity is restricted to cases in which the incident and diffracted rays lie in a plane which is perpendicular to the grooves (at the center of the grating). Where G = 1/d is the groove frequency or groove density, more commonly called "grooves per millimeter".Įq. It is sometimes convenient to write the grating equation as
The special case m = 0 leads to the law of reflection β = – α. For a particular wavelength λ, all values of m for which |mλ/d| < 2 correspond to propagating (rather than evanescent) diffraction orders. Here m is the diffraction order (or spectral order),which is an integer. Which governs the angular locations of the principal intensity maxima when light of wavelength λ is diffracted from a grating of groove spacing d. These relationships are expressed by the grating equation At all other angles, the Huygens wavelets originating from the groove facets will interfere destructively. The principle of constructive interference dictates that only when this difference equals the wavelength λ of the light, or some integral multiple thereof, will the light from adjacent grooves be in phase (leading to constructive interference). The geometrical path dif-ference between light from adjacent grooves is seen to be d sin α + d sin β. Other sign conventions exist, so care must be taken in calculations to ensure that results are self-consistent.Īnother illustration of grating diffraction, using wavefronts (surfaces of constant phase), is shown in Figure 2-2. For either reflection or transmission gratings, the algebraic signs of two angles differ if they are measured from opposite sides of the grating normal.
#Wavelength from grating and diffraction angle formula plus#
In both diagrams, the sign convention for angles is shown by the plus and minus symbols located on either side of the grating normal. By convention, angles of incidence and diffraction are measured from the grating normal to the beam.
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