intensity and double slit experiment questions?

Question

1) Looking at the equation for intensity I=4(I sub o)cos(pi*d*y/wavelength*L)^2, as you increase the distance between the screen and the 2 slits why does intensity increase?

2) Also if you increase the slit width, by the equation, the intensity doesn't change. Intuitively I thought it should change intensity somehow.

3)If you increase only one slit width of the two slits, the intensity should be skewed somehow. How is it changed?

Answer 1

1. The denominator of the argument to the cosine is (wavelength*L), correct? Since y ~= θL increases approximately as L does, the cos^2 part doesn't change very quickly with L. Meanwhile Io (I sub zero), the intensity of the central peak, decreases in inverse proportion to increasing L. So I decreases with increasing L.
2. I would too. I think the intensity equations are limited to the ratio I/Io where Io is the central peak value, and don't address the actual value of Io. Although this hardly counts as proof, the calculator at the ref. page shows increasing visual intensity in its "spectrum" display as slit width goes from 1 to 12 microns, while the plotted intensity maximum doesn't change. I suspect the plot is actually of I/Io.
3. I don't have any idea about the different-widths response, but it might be that of two equal slits whose width is some weighted mean of the two widths. That needs more thought.