Diffraction grating

It's not too hard to convince yourself that that angle theta is actually the same as the angle between all these lines and the vertical.

So the difference between all of these lengths, and this is really the key lesson of diffraction gratings, looks like d times the sine of that angle.

In particular, if it was the case that this key expression, d times the sine of theta, happened to be exactly the wavelength of the light, commonly denoted lambda, all of the beams emanating from these different slits are going to be in phase with each other, so they'll constructively interfere at the point we're analyzing.

This is why, even though in the immediate vicinity you have this chaotic mess that's very hard to describe, zoomed out a sufficient distance away, you have a distinct beam along a certain direction.

If you've ever noticed how the reflections off of a DVD or a CD produce this rainbow pattern, It's essentially the same effect going on there.

The angle of reflection depends on the spacing between the ridges and the wavelength of the light.

So that's the packaged lesson about diffraction gratings, but now let's zoom out and remember why we were doing this.

If you record a hologram of a simple point in space, the exposure pattern on the film is this Fresnel zone plate.