# Basic, intuitive explanation for a diffraction grating

I am tutoring a high school student in physics, and struggling to find a good explanation as to why the interference pattern from a diffraction grating has thinner maxima compared to a double slit.

Does anyone have an explanation of this that an average high school physics student could understand? The content they have covered just includes the basics of Young's double slit experiment - no single slit interference or mathematical derivations of the interference equation ($d \sin \theta = n \lambda$). An ideal explanation would include very little maths (ideally none), and be somewhat intuitive to understand. Cheers

• Did you prove that the slit width and the distance between the slits are the same in the double slit obstacle and in the diffraction grating? – HolgerFiedler Nov 18 '17 at 5:04
• Yes, but that is part of what makes the whole thing so hard to explain: that equation suggests no differences if $d$ is kept constant – Jordan Nov 18 '17 at 5:22

Another method: you can state without proof that for $n$ slits, there are $n-1$ points of destructive interference between any two points of destructive interference. (For your own purposes: you can show this graphically with phasors and drawing regular polygons with said phasors). If we think of a diffraction grating as infinity slits next to each other, this implies that there are infinite points of destructive interference between any two points of constructive interference and so intuitively every point that's not constructive is destructive.