Diffraction Grating Formula

A diffraction grating defines an optical component with a periodic structure that splits the light into various beams that travel in different directions. It is an alternative way to observe spectra other than a prism. Generally, when light is incident on the grating, the split light will have maxima at an angle θ.  The formula for diffraction grating is used to calculate the angle.

Diffraction grating formula

diffraction grating formula

Where,

  • n is the order of grating,
  • d is the distance between two fringes or spectra
  • λ is the wavelength of light
  • θ is the angle to maxima

Solved Examples

Question 1: A diffraction grating is of width 5 cm and produces a deviation of  30in the second-order with the light of wavelength 580 nm. Find the slit spacing.

Solution:

Given: Angle θ =300, order n = 2, wavelength λ = 580 nm.

The slit spacing is given by,

diffraction grating formula 1

d = 2×580×10-9 /sin 

diffraction grating formula 3 m

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