# Basic formula for diffraction grating

1. Feb 27, 2013

### Outrageous

1. The problem statement, all variables and given/known data
For the diffraction grating that used to detect the wavelength of a wave, we use d sinθ= nλ.
When we find r1-r2 to get nλ.
1) What is the assumption we should make?
2)Then why r1-r2 will get λ?

2. Relevant equations
d sinθ= nλ

http://physicsed.buffalostate.edu/pubs/StudentIndepStudy/EURP09/Young/Young.html
3. The attempt at a solution
I think we should assume r1 = r2
I think from the second diagram , the first order formed due to the difference between the wavefront of 2 slits is one wavefront( same as one wavelength)?

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Last edited: Feb 27, 2013
2. Feb 27, 2013

### cepheid

Staff Emeritus
Not quite. If r1 equalled r2, then there would be no interference, because the waves from each slit would travel exactly the same distance and arrive in phase.

However, there is something about r1 and r2 that you are meant to assume. Hint: what happens to the angle between the two paths when L >> d?

3. Feb 27, 2013

### Outrageous

Do you mean id the value of r1 equal to r2 ? Or u mean if r1 and r2 are parallel?
Even there is only one slit ,there is interference, how come there will be no interference?

However, there is something about r1 and r2 that you are meant to assume. Hint: what happens to the angle between the two paths when L >> d?[/QUOTE]

r1is almost same as r2, if L>>d ,then r1 is almost parallel to r2.

4. Feb 27, 2013

### haruspex

In the first diagram, call the points: A where r1 and r2 meet; B the other end of r2,; C the other end of r1; D the point where the perpendicular from B to AC hits AC.
You have CD = d sin theta; AD = r1 - d sin θ = r2 cos θ.
What do you know about the behaviour of cos θ for small θ?

5. Feb 27, 2013

### Outrageous

I got it~~cos θ for very small θ will get one. So we can prove that r2=AD.
Then the second thing I dont understand is that the AC-AB= λ, why ? Is that because from the second diagram , the first order formed due to the difference between the wavefront of 2 slits is one wavefront( same as one wavelength)
Thank you.

6. Feb 27, 2013

### haruspex

Yes.

7. Feb 27, 2013

### Outrageous

thank you so much