Basic formula for diffraction grating

[Outrageous]

Homework Statement

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?

Homework Equations

d sinθ= nλ

http://physicsed.buffalostate.edu/pubs/StudentIndepStudy/EURP09/Young/Young.html

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)?
Please guide . Thank you

 

[cepheid]

Homework Statement

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?

Homework Equations

d sinθ= nλ

http://physicsed.buffalostate.edu/pubs/StudentIndepStudy/EURP09/Young/Young.html

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?
Please guide . Thank you

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?

 

[Outrageous]

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.

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.

Please guide, thanks

 

[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?

 

[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 don't 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.

 

[haruspex]

Then the second thing I don't 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.

Yes.

 

[Outrageous]

thank you so much