Diffraction with a large array of slits

[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).

Homework Statement

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.

Homework 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.

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

 

[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?

 

[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.

Thanks for the reply btw.

 

[dauto]

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

 

[unscientific]

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.

Thanks for the reply btw.

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?