Diffraction Grating - Resolving Power

[Darth Frodo]

Homework Statement

4. Light from a mercury discharge lamp contains 2 yellow lines at 577 nm and 579 nm. Find the angle of diffraction for the 577 nm line in second order when passed through a grating having 2400 lines at 80 lines per mm.
What is the expected dispersion in second order in the vicinity of this line?
What is the resolving power in second order?

The Attempt at a Solution

Ok so the first part was grand. I'm having trouble with the second part,

$R = \frac{λ}{Δλ} = Nm$

This gives me 2 very different answers though. Which one is applicable and why? I mean, they are obviously only equal at one value for m but I don't know.

 

[Darth Frodo]

Shameless Bump

 

[SammyS]

Homework Statement

4. Light from a mercury discharge lamp contains 2 yellow lines at 577 nm and 579 nm. Find the angle of diffraction for the 577 nm line in second order when passed through a grating having 2400 lines at 80 lines per mm.
What is the expected dispersion in second order in the vicinity of this line?
What is the resolving power in second order?

The Attempt at a Solution

Ok so the first part was grand. I'm having trouble with the second part,

$R = \frac{λ}{Δλ} = Nm$

This gives me 2 very different answers though. Which one is applicable and why? I mean, they are obviously only equal at one value for m but I don't know.

Homework Statement

Homework Equations

The Attempt at a Solution

You're not assuming that Δλ = 2 nm, are you?

Shameless Bump

Yes. You waited nearly long enough for a legal bump.

 

[Darth Frodo]

Yes, I am assuming that Δλ = 2 nm. Why? I assume this is incorrect?

 

[SammyS]

Yes, I am assuming that Δλ = 2 nm. Why? I assume this is incorrect?

2 nm is what you need to be able to resolve. -- i.e. your resolving power needs to be λ/(Δλ) .

The resolving power of the grating in second order is (m)(N) .