At a late stage in the spiral double slit project, I suddenly realised I should ‘sanity check’ my results against the equations we learned in high school for the double slit experiment.
I then had a small panic attack when my numbers didn’t match up…
After spending a day digging through my code & notes looking for errors, and plotting out different simulations, I suddenly realised why my numbers weren’t working. This is the equation we learned in high school:
Essentially it describes the locations that satisfy the Bragg condition, that is, the locations where the phases differences of the two signals reinforce (0 degrees) , or cancel out (180 degrees).
However there’s a gotcha here. The vectors contributed by each slit aren’t constant in length, but vary in a Sinc pattern along the screen.
So, with that in mind, let’s see how my simulation matches the high school version. The animation shows what happens if the slit width is varied, but everything else is kept constant.
The blue dots are the Bragg condition for cancellation. The green line should always touch the dots if they’re a good predictor for the trough locations on the screen.
As you can see the equation doesn’t predict all the trough locations by a long shot. It’s certainly better than nothing, but by itself the Bragg condition (phase information) doesn’t tell the whole story as far as interference is concerned. The magnitude information also need to be taken into account.