A diffraction grating is a type of optical instrument obtained with a continuous pattern. The number of lines per mm in the diffraction grating is 326.
A diffraction grating is a type of optical instrument obtained with a continuous pattern. The pattern of the diffracted light by a grating depends on the structure and number of elements present.
The given data in the problem is
[tex]\theta[/tex] is the angle formed between the path of the incident light and the diffracted light = 9. 2°
λ is the wavelength of the light=490nm=4.9
N is the number of lines per mm in the diffraction grating=?
n is ordered = 1
The formula for diffraction grating will be
[tex]\rm n\lambda=dsin\theta\\\\ \rm d=\frac {n \lambda}{sin\theta} \\\\ \rm d=\frac {1\times4.90\times10^{-7}}{sin9.2^0} \\\\\rm d=3.06\times10^{-6}m=3.06\times10^{-3}mm[/tex]
The number of lines per mm is the inverse of the distance between grating in mm.
[tex]\rm N=\frac{1}{d}[/tex]
[tex]\rm N=\frac{1}{3.06\times10^-3}\\\\\rm N=326.8/mm[/tex]
Hence the number of lines per mm in the diffraction grating is 326.
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