Measurement of wavelength of a laser (He-Ne) light using single-slit diffraction

Light behaves not only like a wave but also like a particle. One consequence of this wave nature is diffraction, where light bends slightly as it travels around the edges of an object. Fraunhofer diffraction, a specific type of diffraction, occurs when parallel light waves from a distant source pass through a small opening or diffracting object, and the resulting pattern is observed on a screen at a far distance. This distant observation is crucial for the characteristics of Fraunhofer diffraction.

In Fraunhofer diffraction the source and the screen are a infinite distance from the obstacle and the wavefront is plane. Let a parallel beam of monochromatic light of wavelength be incident normally upon a narrow-slit AB of width e where it gets diffraction in below fig. if a lens L is placed in the path of the diffraction beam, a real image of the diffraction pattern is formed on the screen MN in focal plane of the lens. BE= AB sin𝜃= e sin𝜃
The corresponding phase difference= (2𝜋/ λ) *path difference = (2𝜋/ λ) * (e sin𝜃)
Now, consider the width AB of the slit divided into n equal parts. Each part forms an elementary source. The amplitude of vibration at P due to the wave from each part will be the same, and the phase difference the waves from any two consecutive parts is, image1
Hence, resultant amplitude at P is given by,
image2
Since, the magnitude intensity at any point in the focal plane of the lens is a function of 𝒂 and 𝜽.so, we obtain a series of maxima and minima.
Condition for a maximum (approximation):

  1. α = 0° or b sin α ≈ (k + ½) λ
  2. b ... width of slit
  3. α ... angle
  4. k ... order of the maximum (1, 2, 3, ...)
  5. λ ... wavelength
    Condition for a minimum:
  6. b sin α = k λ
  7. b ... width of slit
  8. α ... angle
  9. k ... order of the minimum (1, 2, 3, ...)
  10. λ ... wavelength
    image3
    Fig. 1
    image4
    Fig.2