# Diffraction with a large array of slits

1. May 28, 2014

### Flucky

Hi all, exams soon and I'm stressing out over this small question. If anyone could guide me through, explaining why you're doing what you're doing that'd be beyond great. I posted this in the introductory thread but with no replies thought I should move it here (unsure of how to delete the other one).

1. The problem statement, all variables and given/known data
Light of wavelength λ is incident normally on a screen with a large array of slits having
equal widths b, and periodically displaced by a distance a.

(i) Find the maximum diﬀraction order which can be observed using this system of slits.

(ii) Find the minimum period a for which diﬀraction can be observed for light with
wavelength λ = 10µm.

2. Relevant equations
AFAIK the only equation relevant is asinθ = mλ

One that has cropped up is sinθ$\pm1$ = $\pm\frac{λ}{b}$ , although there is no explanation next to this one so I'm not sure what it means.

3. The attempt at a solution
Initial thoughts are to set θ = 90° as it's asking for a maximum. Past this I don't know where to go

Last edited: May 28, 2014
2. May 28, 2014

### unscientific

For part (i): you are right, because the maximum angle is 90 degrees.

Part (ii): What happens when width of slit approaches the distance between slits?

3. May 28, 2014

### Flucky

From the second equation it looks like as the slit width increases the angle between maxima will decrease. Am I able to set the two equations equal to each other? If so as slit width approaches slit separation the diffraction order will go to 1.

4. May 28, 2014

### dauto

I don't think the second equation makes any sense. All you need is the first one.

5. May 28, 2014

### unscientific

When the separation of slits approaches the slit width, the two slits become one - meaning it is a single slit diffraction. We can't let that happen, $a$ has to be bigger than the width of a slit, $b$.

Conversely, when the width of the slit approaches the separation, the two slits become one - meaning it is a single slit diffraction. We can't let that happen, so $b$ has to be smaller than slit separation of slits, $a$.

Thus, to answer your question - what is the smallest possible value of $a$, in order for multiple slit diffraction to occur?

Last edited: May 28, 2014