Referring to Figure 2, there will be three diffracted orders ( m = –2, –1, and +1) along with the specular reflection ( m = 0). As an example, suppose a HeNe laser beam at 633 nm is incident on an 850 lines/mm grating. The larger the period Λ, or the lower the frequency f, the more orders there are. (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. Therefore, the wavelength of light will ne 146.7 nano meter.Gratings are based on diffraction and interference:ĭiffraction gratings can be understood using the optical principles of diffraction and interference. In this formula, \(\theta\) is the angle of emergence at which a wavelength will be bright. This is known as the DIFFRACTION GRATING EQUATION. Constructive interference will occur if the difference in their two path lengths is an integral multiple of their wavelength \(\lambda\) i.e., The formula for diffraction grating:Ĭonsider two rays that emerge making the angle \(\theta\) with the straight through the line. Diffraction is an alternative way to observe spectra other than a prism. Also, if peaks fall on peaks and valleys fall on valleys consistently, then the light is made brighter at that point. If a peak falls on a valley consistently, then the waves cancel and no light exists at that point. Here Huygens’ Principle is applicable.Īccording to it every point on a wavefront acts as a new source, and each transparent slit becomes a new source so cylindrical wavefront spread out from each. Rays and wavefront form an orthogonal set so the wavefront will be perpendicular to the rays and parallel to the grating. 2 Solved Examples Diffraction Grating Formula Concept of the diffraction gratingĪ parallel bundle of the rays will fall on the grating.
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