# 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.

Thank you in advance

• 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? Aug 23, 2018 at 15:11
• By primary source of light I mean S0. Aug 25, 2018 at 2:21

## 2 Answers

The width of the slit apertures does not affect the spacing of the fringes in the interference pattern, but it does affect the fringe contrast. In effect, the fringes in the interference pattern are blurred by an amount corresponding to the widths of the slit apertures.

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.