# Young's double slit experiment, slit separation

I just wrote a test and there was a question on young's double slit experiment...we were given the width of the slits and the sepration between their centres

My question is...In making calculations involving slit seperation,say "a"...will "a" just be the seperation between their centres or is it necessary to subtract the value of the width from the sepration between the centresto get the value of a...I checked my textbook but there isn't anything about that

• That depends on the detail of your calculation. Do you account for the width of the slits in your calculation? Or do you treat them as infinitesimally thin? I'm guessing the latter, in which case that should answer your question... Nov 14, 2017 at 15:26
• Well...it looks a bit complex because there are some terms i'm not really sure to understand...but the actual question was to find the fringe seperation...and from what you said I guess we were just meant to use the distance between the centres to solve the question Am i right?
– Lee
Nov 14, 2017 at 16:16
• Yes the main fringe spacing is determined by the center to center spacing of the slits. Nov 14, 2017 at 17:12

Usually when you compute the diffraction pattern of two slits of finite width, you consider the aperture to be the convolution of two infinitesimal slits, and a finite aperture. Now as you may know, the Fraunhofer diffraction pattern is the Fourier transform of the aperture function. The convolution theorem tells us that the Fourier transform of a convolution of two functions is the product of the Fourier transforms of the individual functions.

What that means is that if you consider the centers of the slits to be a distance $a$ apart, and they each have a width $w$, then the diffraction pattern will be the product of the pattern you expect from two infinitesimal slits that are distance $a$ apart, and the diffraction pattern of a single aperture of width $w$.

This will look like a cosine function (spacing determined by $a$) whose amplitude is modulated by a sinc function (shape determined by $w$).

See for example this question.