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# 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

- Intensity pattern for single slit diffraction:

where

- Intensity pattern for double slit interference:

where

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

- Remember that in the double slit interference analysis we (implicitly) assumed that the two slits were "point" wave sources. Of course in reality this is impossible, no sources are true "point" sources. An accurate description of double slit interference must include the effect of the finite width of each slit - that is, the diffraction phenomena from each slit. A detailed mathematical analysis leads to an intensity pattern at point P given by,

> Qualitatively, the interference pattern is modulated by the diffraction pattern, as indicated below.

> Note that the slit width "a" must be smaller than the slit separation "d" (center to center).

> The number of interference maximum underneath the central maximum of the diffraction envelope depends on the relative values of a and d.
> 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

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