Question #181396

Explain YDSE


1
Expert's answer
2021-04-19T17:12:06-0400

Young's Double Slit Experiment (YDSE)


\bull For an interference pattern to be observable,


  • The waves must be of the same type and must meet at a point.
  • The waves are coherent, i.e. the waves from each source maintain a constant phase difference.
  • The waves must have the same wavelength and roughly the same amplitude.
  • The waves must be both either unpolarised or have the same plane of polarisation.



\bull Two sources are said to be coherent

if waves from the sources have a constant phase difference between them.



\bull Young’s Double Slit Experiment A simple experiment of the interference of light was demonstrated by Thomas Young in 1801.


\bull It provides solid evidence that light is a wave.




Interference fringes consisting of alternately bright and dark fringes (or bands) which are equally spaced are observed. These fringes are actually images of the slit.







At O, a point directly opposite the mid-point between S1 and S2, the path difference between wavesS2OS1OS_2O – S_1O is zero.

Thus constructive interference occurs and the central fringe or maxima is bright.


Suppose P is the position of the nth order bright fringe (or maxima). The path difference between the two sources S1 and S2 must differ by a whole number of wavelengths.

S2PS1P=nλS_2 P –S_1 P = nλ


As the distance D is very much larger than a, the path difference S2PS1PS_2 P – S_1 P can be approximated by dropping a perpendicular line S1 N from S1 to S2 P such that S1PNPS_1 P ≈ NP


and

the path differenceS2PS1PS2N=nλ\boxed{ S_2 P –S_1 P ≈ S_2N = nλ}


From geometry, S2N = a sin θ where a is the distance between the centres of the two slits.

Equating, a sin θ = nλ and re-arranging,


sinθ=nλa\boxed {sin θ = {nλ\over a}}


But from geometry,

tanθ=xnD\boxed{tan θ = {x_n \over D}}

where xn = distance of nth order fringe from the central axis Since θ is usually very small,


tan θ ≈ sin θ

i.e. xnD=nλa\boxed{{ x_n \over D} ={ nλ\over a }} or xn=nλDa\boxed{x_n= {nλD\over a}}



Thus the separation between adjacent fringes (i.e. fringe separation) is,


Δx=xn+1xn=(n+1)λDanλDa=λDa\boxed{Δx = x_{n+1} – x_n ={ (n+1) λ D\over a }– {nλ D\over a} ={ λD\over a}}



Thus,

Fringe separation Δx=λDa\boxed {Δx ={ λ D\over a}}



Clearly Δx is a constant if λ, D and a are kept constant. If all factors are kept constant, the fringes are evenly spaced near the central axis.



various diagrams








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