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Young’s Double Slit Experiment (YDSE)

Monochromatic light (single wavelength) falls on two narrow slits S1 and S2 which are very close together acts as two coherent sources, when waves coming from two coherent sources (S1S2) superimpose on each other, an interference pattern is obtained on the screen. In YDSE, alternate bright and dark bands obtained on the screen. These bands are called fringes.
Fig. 9
  • Central fringe is always bright because at central position, φ = 0° or Δ = 0
  • The fringe pattern obtained due to a slit is more bright than that due to a point.
  • If the slit widths are unequal, the minima will not be complete dark. For very large width, uniform illumination occurs.
  • If one slit is illuminated with red light and the other slit is illuminated with blue light, no interference pattern is observed on the screen.
  • If the two coherent sources consist of object and it’s reflected image, the central fringe is dark instead of bright one.
Fig. 10

Useful results

Path difference Path difference between the interfering waves meeting at a point P on the screen is given by
Δ = Δi + Δf
where Δi = initial path difference between the waves before the slits and Δf = path difference between the waves after emerging from the slits. In this case, Δi = 0 (commonly used condition). So
where x is the position of point P from central maxima.
For maxima at P: Δ = ; where n = 0,  1,  2, … and For minima at P : 94838.png, where n = 1, 2, …
Location of fringe Position of nth bright fringe from central maxima, 94847.pngn = 0, 1, 2 …
Position of nth dark fringe from central maxima
94853.png; n = 1, 2, 3 …
Fringe width (β) The separation between any two consecutive bright or dark fringes is called fringe width. In YDSE, all fringes are of equal width (Fig. 11). Fringe width, β = λD/d, and angular fringe width θ = λ/d = β/D.
Fig. 11
In YDSE, if n1 fringes are visible in a field of view with light of wavelength λ1, while n1 with light of wavelength λ2 in the same field, then n1λ1 = n2λ2.
Separation (Δx) between fringes
  • Between nth bright and mth bright fringes (n > m), Δx = (n – m)β
  • Between nth bright and mth dark fringe
    If n > m, then 94859.png
    If n < m then 94865.png

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