# Diffraction Grating, Maxima, finding slit seperation

• Oijl
In summary, incident light with a wavelength of 680 nm is diffracted by a grating, resulting in adjacent maxima at angles given by sin θ = 0.2 and sin θ = 0.3. The fourth-order maxima are missing. The smallest slit width this grating can have can be found using equations that relate slit width to angle theta, with the condition that m2=m1+1. The information that the maxima are adjacent is enough to determine both d (slit width) and m1, m2 (diffraction orders). In the second part of the problem, the same equation can be used to find the minimum size of the slit, with the condition that there are only

## 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?

## The Attempt at a Solution

What equations relate slit width to angle theta?

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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).

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.

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

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.

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.