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So, my understanding is that in Young's experiment you first have a single slit, which helps you create the point source and then the two slits. My question is: what happens when you take out the first slit and let light come from an extended source? This was a conceptual question in a homework and I was discussing it with some classmates. Personally I think you wouldn't see an interference pattern unless the source was very small, because of spatial incoherence. Just how small or if it even depends on the length of the source is what I'd like to know.

Níckolas Alves
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Walu
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  • Duplicate? https://physics.stackexchange.com/questions/331572/why-must-the-single-slit-in-a-double-slit-experiment-be-narrow/331672#331672 – Farcher Nov 24 '17 at 07:41

1 Answers1

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You are correct that the interference pattern will be lost, unless the source is spatially coherent.

Formation of the interference pattern requires

  1. Spatial coherence , like you mentioned.
  2. Temporal coherence - Monochromatic with constant phase difference between the sources.

Now, how does the size of an extended source determine spatial coherence? Consider a monochromatic extended source of lateral size $l$ as shown below.

enter image description here For each of the slit $S_1$ ans $S_2$, if the path difference from $S'$ differ by half wavelength compared to that of $S$ then the interference pattern produced by $S$ gets nullified by that produced by $S'$. This is since the maxima of $S$ overlaps with the minima of $S'$, and vice versa.

$S'S_1 - S'S_2 = \lambda/2$
$S'S_1 - S'S_2 = d\sin\alpha \approx d\alpha \approx dl/a$
$dl/a = \lambda/2 => l = \lambda a/2d$

We have not yet considered points in between S and S' of the extended source.

Using the same argument, if the source width $l$ was twice $SS'$ then every point in between $SS'$ will have a corresponding point that exhibits a path difference of half a wavelength so as to make the interference pattern disappear.

That is, if $l = 2* \lambda a /2d $, the interference pattern disappear.

If so, then what will give a good interference pattern?
It will be when $l << \lambda a /d$
(so that not all points in the extended source do not have a corresponding point that nullifies its interference pattern).

lambda
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