![]() ![]() (2) A graphical example of the grating equation: Figure 2 In terms of f the grating equation becomes Often gratings are described by the frequency of grating lines instead of the period, where f (in lines/mm) is equal to 10 6/Λ (for Λ in nm). For a given angle of incidence, θ, it gives the angle of diffraction θ m for each “order” m for which a solution to (1) exists. Since AB = Λsinθ m and A’B’ = Λsinθ, where Λ is the grating period and θ m and θ are the angles of diffraction and incidence, respectively, relative to the surface normal, the condition for constructive interference is Mathematically, the difference between paths AB and A’B’ is a multiple of the wavelength when AB – A’B’ = mλ, where m is an integer and λ is the wavelength of light (typically stated in nm). If the difference between adjacent green-blue ray paths diffracted off of identical locations on adjacent periods is equal to a multiple of the wavelength of light, the two blue rays interfere constructively. The light is diffracted in many directions, only one of which is indicated by the blue rays. ![]() Referring to Figure 1, imagine a beam of light represented by the two green rays incident on the binary (rectangular profile) grating shown. Constructive interference leads to the grating equation: Figure 1 If the surface irregularity is periodic, such as a series of grooves etched into a surface, light diffracted from many periods in certain special directions constructively interferes, yielding replicas of the incident beam propagating in those directions. When light is incident on a surface with a profile that is irregular at length scales comparable to the wavelength of the light, it is reflected and refracted at a microscopic level in many different directions as described by the laws of diffraction. Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference. ![]()
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