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Sodium light has two wavelengths 589 nm and 589.6nm, as the path difference increases when is the visibility of fringes a minimum?

Sodium light has two wavelengths 589 nm and 589.6nm, as the path difference increases when is the visibility of fringes a minimum?

Grade:12

1 Answers

Arun
25750 Points
6 years ago
Fringe maxima will occur when dsinθ = mλ
Fringe minima will occur when dsinθ = (m+1/2)λ
where m is the fringe order.
The fringe pattern will consist of a superimposed pattern of fringes from the 589.6 nm line and the 589.0 nm line, with the fringes from the 589.0 nm line being slightly more closely spaced than fringes from the 589.6 nm line.
Fringes will be minimally visible when maxima from the first fringe pattern are superimposed on minima from the second fringe pattern.
589.6×m≈589.0×(m+0.5)
589.6×m≈589.0×(m+1.5)
etc.
The fringe pattern will fade out around the 491st order, then will fade back in, then will fade out around the 1472th order, and so on.
Since the coherence length of the sodium D lines is only around a millimeter or so, one wouldn’t expect to be able to follow the fade-in/fade-outs for much longer than that.
More than a century ago, Albert Michelson simulated fringe patterns produced by spectral lines of varying degrees of complexity using a then state-of-the-art harmonic analyzer that he had designed. He noted that each component of the sodium D line was itself a doublet, so that the fringe pattern produced by a sodium source more resembled (3) than it did (2).
 

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