With a few good demonstrations in the lab, and with the back up of a good animation like that put together by PHET, I find that most students can grasp the basic idea of Young's Double Slit experiment. And diligent students will usually manage to work their way through the derivation of the grating formula.
But a detailed understanding of the maths that underpins the grating formula is another matter, and I'm inclined to think that many who do quite well on this material still lack any real understanding of the geometry involved and how exactly the interference pattern is formed. And I wouldn't blame them. It certainly took me a long, long time reading about coherent waves, the path difference of between light rays and how they relate to the angles involved before I had wrapped my head around it all.
But I was trying to learn it all in the pre-internet age with rudimentary, static diagrams representing complex, dynamic situations. And in the internet age, things don't have to be so torturous. So I was delighted when the always ingenious Rory Geoghegan showed me a great interactive demonstration that he had put together using GeoGebra that allowed users to investigate how and when (and where) interference will lead to a bright fringe and when it won't. With a few easily managed controls, it allowed us to change wavelength, d values and our position on the screen.
But sadly, I can't seem to link to it!
Nevertheless, in searching for it, I came across a number of similar interactives on GeoGebra which each approach the problem in slightly different ways. I've linked to them all below, and I'll add in Rory's as soon as I can figure it out. I so wish I had had access to wonders such as these is in the early eighties!
You might need to download GeoGebra itself first: App Downloads – GeoGebra