Diffraction grating and Dirac comb

1. Nov 3, 2014

SarahLou

1. The problem statement, all variables and given/known data
I need to measure (with the ruler) the width the depicted sinc envelope and the period of the depicted Dirac comb light pattern.

And from the above I need to calculate the width of one slit a (i.e. aperture width) of the grating, and the period of the grating dx (i.e. distance between each slit). I have no idea where to start :(

2. Relevant equations

3. The attempt at a solution
I suck at physics and spent few hours reading everything I could find on the internet on convolution, diffraction and fourier theorem. I still have no clue what I need to measure!

2. Nov 3, 2014

vela

Staff Emeritus
What quantities can you measure from the diffraction pattern?

3. Nov 3, 2014

SarahLou

distance between each point? I really don't know :/

4. Nov 3, 2014

SarahLou

I forgot to mention the distance between the slit and the points on the paper was 1000mm and the wavelength was 633nm. I tried to calculate width of one slit a = 9Lλ/0.31 = 9(1000)0.000633/0.31= 18.3mm

5. Nov 3, 2014

vela

Staff Emeritus
Which of the six figures does the photo of the diffraction pattern correspond to?

6. Nov 3, 2014

vela

Staff Emeritus
You mention two distances. Which one was 1000 mm? Do you realize that 1000 mm is 1 meter? I doubt the slits or the points on the paper were 1 meter apart.

7. Nov 4, 2014

SarahLou

There was 1 metre distance between the slit frame and the photographic paper that recorded the diffraction. 1 metre allowed the points to be perfectly focused. Six figure distraction is corresponding to the last image on the right I think, and I'm guessing the middle one above it corresponds to the slits and the distance between them?

8. Nov 6, 2014

vela

Staff Emeritus
Ah, okay, I totally misread what you wrote. I took it to mean the distance between the points was 1 m or the distance between the slits was 1 m whereas you meant the distance from the slits to the screen is 1 m.

You're right that the diffraction pattern corresponds to the figure on the bottom right, so by measuring the distance between the points, you can get a measure of what $\delta \omega$ is. Since $\delta x$ and $\delta \omega$ are related, you can, in principle, be able to figure out what $\delta x$ is. Note, however, that you can't actually measure what $\delta \omega$ is with the ruler; you're only getting a quantity that's proportional to $\delta \omega$. If you don't see why that's the case, consider the units of $\delta \omega$. So part of your task is to figure out how $\delta \omega$ is related to the linear distance between the points on the screen.

Do you see what you would measure on the diffraction pattern to figure out what $a$ is?