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?
Best Answer
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.