# Effect of aperture of source slit on the interference pattern observed in Young's Double Slit experiment

The following describes the YDSE set-up:

The fringes formed on the screen have certain finite width which can be calculated on the basis of the following formula:

• $$\beta = \lambda*D/d$$ $$where: \beta = Fringe..Width$$ $$\lambda = Wavelength..of..light$$ $$D= Distance..between.. the.. slits.. and.. the.. screen$$ $$d= Distance.. between.. the.. two.. sources$$

This formula does not give any relation between the aperture of the primary source of light and the interference pattern.

## My question is two part:

1. Does changing the size of aperture effect the interference pattern?
2. Is there a formula that describes the relation between the aperture and the interference pattern?

I tried to find answer on wikipedia and Fundamentals of Physics by David Halliday, Robert Resnick, and Jearl Walker but couldn't find any.

I personally feel that it should not effect the interference pattern but I am not sure.

• What exactly do you mean by aperture of the primary source of light ? Is it the widths of slits $S_1 and S_2$ or you refer to something else? Commented Aug 23, 2018 at 15:11
Young's double slit experiment assumes $S_1$ and $S_2$ radiate light of the same phase and amplitude. The portion of the experiment to produce such light (left to the second screen in your picture) is usually considered a technical issue and does not affect the final interference pattern.
In your particular scheme, if $S_0$ is narrow enough and the distance between first and second screen is large enough, the phase/amplitude assumptions regarding light on $S_1$ and $S_2$ are probably met.
However, if $S_0$ is large enough and it is being illuminated by a plane wave (as suggested by the figure), there may already be diffraction effects at this preliminary stage. For example, slots $S_1$ and $S_2$ may fall within the nodes (black spots) of the diffraction from $S_0$. This would have a large effect on the final interference pattern.