# Why does moving the source-slit closer to the double-slit plane decrease the sharpness of the interference-pattern?

Thomas Young used a single-slit plane before the two-slits plane in order to make the light source coherent.

My book (NCERT Physics II) presents the above query and writes:

Let $s$ be the size of the source-slit and $S$ its distance from the plane of two slits. For interference fringes to be seen, the condition $$\dfrac{s}{S}\lt \dfrac{\lambda}{d}$$ should be satisfied; otherwise, interference patterns produced by different parts of the source overlap and no fringes are seen. Thus, as $S$ decreases (i.e. the source slit is brought closer), the interference pattern gets less and less sharp, and when the source is brought too close for this condition to be valid, the fringes disappear.

I've totally failed to comprehend what the book is saying. I also don't know how it deduced the inequality relation. Can anyone please explain me what is the reason for this phenomenon? Also, can anyone tell me how the inequality relation was deduced? What does it mean by sharpness of the interference pattern?

I believe the reason for this "rule of thumb" is that Young didn't have lasers to work with :-), so he had to use a white-light source. The farther away you place the source slit, the smaller portion of the solid angle output reaches the double slit. There is, to some extent, local coherence in the source, so by reducing the spatial portion of its output you increase the coherence of the light passing through the double slit and thus increase the visibility of the final interference pattern.

"Sharpness" of pattern refers to this visibility parameter. If you have perfect coherence, you'll get peaks of some intensity and nulls of zero intensity. The incoherent "background" is spatially uniform (to first order) and thus reduces the SNR, i.e. the difference between intensity peaks and minima is smaller relative to the average intensity. It's like an AC signal riding on a DC pedestal.

• Firstly, thanks for the answer; I'm not conceiving your statement: "There is, to some extent, local coherence in the source, so by reducing the spatial portion of its output you increase the coherence of the light passing through the double slit"; sorry, but can you please explain this line especially the bold one? Also, I would be grateful if you explain the line also: "The farther away you place the source slit, the smaller portion of the solid angle output reaches the double slit"??
– user36790
Sep 3 '15 at 16:25
• Look at it this way: suppose you had a source radiating into a sphere. As the sphere's radius increases (so the source is farther from the sphere's surface), the solid angle covering a given area on the surface gets smaller and smaller. This means that a smaller and smaller portion of a non-point source contributes to the light on a given area on the sphere, and in the limit a point source is self-coherent. Sep 3 '15 at 18:40
• Thanks, for responding, sir. I have understood how the solid angle gets reduced at the two-slits region as the single-slit source is moved away. But I'm not understanding how by reducing the solid angle, coherence is increased. What do you want to mean by "local coherence in the source"? I'm not understanding "local coherence":( However, you deserve +1:|
– user36790
Sep 4 '15 at 3:02