Why Is Calculating Slit Spacing in a Diffraction Grating Confusing?

[embphysics]

Okay, I understand this is a highly trivial problem, yet for some reason, it is bestowing much difficulty upon me.

If a diffraction grating has 500 slits/mm, what is the spacing between each slit?

Evidently the spacing between each slit is given by the inverse of that ratio. I am having trouble grasping this fact. To attempting to gain some insight, I began with something simple: suppose we have two slits, both of which, including the space between them, are 1 inch in length, \displaystyle \frac{2~slits}{1~in}. The inverse of this, \displaystyle \frac{0.5~in}{1~slit}, suggests that there...And this is where the uncertainty comes into play. I would view the ratio as saying that each slit is 0.5 inches in length, and two together would be 1 inch; but this suggests that there is no spacing between.

Could someone possibly help me?

 

[jfizzix]

The spacing in diffraction gratings is usually from the canter of one slit to the center of the next slit.

if you have 500 slits/ mm, you can divide the numerator and denominator both by 500 to get

\frac{500\; \text{slits}}{\text{mm}} (\frac{\frac{1}{500}}{\frac{1}{500}}) = \frac{1\; \text{slit}}{\frac{1}{500}\text{mm}} = \frac{1\; \text{slit}}{2\mu \text{m}}

or about 2 microns from the center of one slit, to the center of the next slit.

 

[embphysics]

So, then this ratio tells me nothing of the spacing between each slit?

 

[haruspex]

So, then this ratio tells me nothing of the spacing between each slit?

That's right. If you know the width of each slit then you can simply subtract that.
But why do you care what the gap between the slits is? It's the distance between slit centres that matters for interference.

 

[embphysics]

Well, I am trying to answer this ostensibly easy lab question, but clearly it isn't turning out to be so. Would it matter that I used the word slit instead of groove?

 

[haruspex]

Well, I am trying to answer this ostensibly easy lab question, but clearly it isn't turning out to be so. Would it matter that I used the word slit instead of groove?

Are you sure the question is literally asking for the gap between the slits? Might it not mean the gap between the slit centres?