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.

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

 

[haruspex]

It's not hard to find articles on the subject on the net. Did you try to follow any of those?

 

[Flucky]

I've had a look all round but can't seem to find anything that helps, unless I'm missing something obvious. I've played around with a few applets as well. The things I found focused on the first equation, and the questions would often be "find the #th maxima" with slit width etc given.

The 90 degrees being a maximum I understand and max diffraction occurs when the slit width equals the wavelength, but for the first part of the question that still leaves me with 3 unknown variables.

Also I created another thread over in the other HW section (https://www.physicsforums.com/showthread.php?p=4758792) thinking I could delete this one. Don't know if the mods would like to merge/delete one.