Double Slit Diffraction/Interference



" All of physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial. "
Ernest Rutherford
eqn1        where        eqn2
eqn1            where        eqn4

Note that φ' = φ/2, where φ is defined in the double slit interference analysis.

eqn5
Qualitatively, the interference pattern is modulated by the diffraction pattern, as indicated below.
fig1
exclamatiom Note that the slit width "a" must be smaller than the slit separation "d" (center to center).
exclamation The number of interference maximum underneath the central maximum of the diffraction envelope depends on the relative values of a and d.

exclamation Diffraction minima occur at θ = λ/a , 2λ/a , 3λ/a...      [ asinθ = nλ ]
         Interference minima occur at  θ = λ/2d , 3λ/2d , 5λ/2d...     [ dsinθ = (n+1/2)λ ]
  • In the examples below the first intensity pattern has  d = 3a, whereas the second pattern has d = (15/2)a

fig2  fig3


  A year after almost failing her high school physics class, a girl told her older brother,
"You know, my physics teacher was right about the optical Doppler effect. You see those cars. The lights of the ones approaching us are white, but the lights of the ones moving away from us are red."


 

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu