# Diffraction grating problem

1. May 15, 2017

### Eagertolearnphysics

1. The problem statement, all variables and given/known data

Yellow sodium light, which consists of two wavelengths, λ_1 =589.0 nm and λ_2 = 589.89 nm, falls on a 7500 lines/cm diffraction grating. Determine (a) the maximum order m that will be present for sodium light, (b) the width of grating necessary to resolve the sodium lines, (c) the grating resolving power in this case, (d) the angular width of each sodium line.
2. Relevant equations

3. The attempt at a solution
(a) I divided λ by Δλ and I found it to be 1000, therefore Nm, where m is the order, will be always larger than λ/ Δλ. therefore i don't get how the problem asks for maximum, however, m = 1 is an answer!
(b) I tried mλ = d sinθ but i don't know what θ to use !!
(c) it depends on (b)

2. May 16, 2017

### CWatters

Perhaps you can explain why you divided λ by Δλ ?

The equation I remember is:
mλ = e * sinθ
where m is the order (1,2,3...)
e is the grating separation
θ is the defraction angle for each m
so
m = e/λ * sinθ

What value of θ gives you maximum m?

3. May 16, 2017

### Eagertolearnphysics

the problem doesn't include the value of θ

4. May 16, 2017

### Biker

What is the maximum angle you can achieve theoretically?

5. May 16, 2017

### Eagertolearnphysics

π/2

6. May 17, 2017

### CWatters

Correct.

So plug that into the equation and calculate m.

7. May 17, 2017

### Eagertolearnphysics

But I don't have the grating separation

8. May 17, 2017

### Biker

You have the number of lines in 1cm.
Can't you use that to find it?

9. May 17, 2017

### Eagertolearnphysics

Yes I can, m = 2.26 but I don't know what to do next !

Last edited: May 17, 2017
10. May 17, 2017

### Eagertolearnphysics

what is the formula for finding angular dispersion of grating? is it the same as angular width?

11. May 17, 2017

### CWatters

You remember that m must be an integer ..