Interference in Two and Three Dimensions

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

Text!

Interference patterns produced by two, closely spaced wave sources in phase. The separation between sources is smaller in the image on the left and larger in the image on the right.

Nodal lines are hyperbolas. Think about it, the definition of a hyperbola is the locus of all points whose distance to two fixed points have a constant difference. At distances much greater than the wavelength, the nodal lines appear as straight radial lines.

Path length difference

constructive	destructive
nλ = Δℓ	(n + ½)λ = Δℓ

General equation

constructive	destructive
nλ = d sin θ	(n + ½)λ = d sin θ

Small angle approximation

constructive	destructive
nλ  ≈  x d L	(n + ½)λ  ≈  x d L

Where …

n = 0, 1, 2, 3, …

is the order

Other Stuff

• interference-overhead.pdf
• Fringes are interference in space. (Beats are interference in time.)
• Use this tone (test-tone-1000.aif) to illustrate interference in the classroom

Summary

• bullet

Problems

practice

1. Write something.
   • Answer it.
2. Write something else.
   • Answer it.
3. Write something different.
   • Answer it.
4. Write something completely different.
   • Answer it.

conceptual

1. Suppose you were the owner of a radio station and that you wanted to extend the range of your broadcast. Would it be wise to erect a second transmitting antenna to broadcast simultaneously with the first? How will a second transmitter affect reception?

numerical

1. problems

Resources

• spectroscopy
  • Mini Spectroscopes, Alan Schwabacher, University of Wisconsin-Milwaukee

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