Interference fringes in Young's experiment

[pfellas]

Homework Statement

Explain why wider slits at the same spacing could produce fringes at the outer edges brighter than some of the fringes nearer the centre.

Homework Equations

fringe spacing = (lamda x D) / slit separation
width of central diffraction fringe = ( 2 x lamda x D ) / aperture width

The Attempt at a Solution

I know that as a slit gets wider the amount of diffraction decreases. I also know that as distance away from the central fringe increases the intensity decreases. I can't put these ideas together to work out why there is brighter fringese further away when logic tells me otherwise.

 

[anathema]

There are a few factors that contribute to this phenomenon. First, let's consider the equation for fringe spacing:

fringe spacing = (lamda x D) / slit separation

As the slit width increases, the slit separation also increases. This means that the fringe spacing will also increase. This wider spacing means that the fringes at the outer edges will be further apart, making them easier to see and giving them a higher perceived intensity.

Secondly, let's look at the equation for the width of the central diffraction fringe:

width of central diffraction fringe = (2 x lamda x D) / aperture width

As the slit width increases, the aperture width also increases. This means that the width of the central fringe will also increase. This wider central fringe will spread out the light more, making the fringes at the outer edges appear brighter in comparison.

Lastly, we have to consider the overall intensity of the light. As you mentioned, as the distance from the central fringe increases, the intensity decreases. This means that the fringes at the outer edges, which are closer to the center, will have a higher intensity compared to the fringes further away.

Combining all of these factors, we can see that the wider slits at the same spacing produce fringes at the outer edges that are brighter than some of the fringes nearer the center due to the wider spacing, wider central fringe, and higher overall intensity.