Diffraction Grating, Maxima, finding slit seperation

[Oijl]

Homework Statement

Light of wavelength 680 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin θ = 0.2 and sin θ = 0.3, respectively. The fourth-order maxima are missing.

(b) What is the smallest slit width this grating can have?

Homework Equations

The Attempt at a Solution

What equations relate slit width to angle theta?

 

[nasu]

The diffraction orders do not have to be 1 and 2. Actually they are not.
You don't need to assume their values. The information that the maxima are adjacent is enough. With your notation, that means m2=m1+1.
You can find both d and m1,m2 from the equations (with the above condition).

 

[Oijl]

Yes, I had tried that, but it gave me values that I thought were too far from the correct answer (which I knew the value of). I've looked at all the numbers more closely, and it's just rounding preferences, is all the matter.

Thanks.

 

[Oijl]

I edited the first post, to make it about the second part of the problem, for which I cannot think of any equations.

 

[nasu]

There is nothing about rounding. The diffraction orders are 1 and 2 (in the first part).
The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
That means that the sin(theta) will have to be l>= 1 for order 4.

 

[nasu]

There is nothing about rounding. The diffraction orders are 2 and 3 (in the first part).
The same equation will give the minimum size of the slit. The condition is that you have only the maxima with orders 0 to 3 and nothing at 4.
That means that the sin(theta) will have to be l>= 1 for order 4.