Calculating the Number of Lines for a Diffraction Grating

[LCSphysicist]

Homework Statement

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Relevant Equations

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A spectral line of wavelength λ = 4,750˚A is actually
a doublet, of separation between the lanes 0, 043˚A . a) which is the smallest
number of lines a diffraction grating needs to have to separate
this doublet in the 2nd order spectrum?

To be honest, i don't know what to do. I first thought that it could have something to do with the Raylegh criterion, but even, so $sin \theta \approx \lambda / D$, and i don't know what would substitute D here. I know it is necessary to show the progress made by the person that made the question, but i would appreciate any tips to realize how to start. Of course, the equation of maximum is $d sin \theta ' = m \lambda$.

 

[phystro]

You can try the following formula, for the resolvance R.
$$ R= \frac{λ}{Δλ}=mN$$
Where λ = 4,750˚A, Δλ= 0, 043˚A, m=2 (second order), and solve for N to find the number of lines.

 

[Charles Link]

Post 2 is a very simple way to do it. Otherwise you can derive the post 2 result by using the formula $I(\theta)=I_o \frac{\sin^2(N \phi /2)}{\sin^2(\phi/2)}$ where $\phi=\frac{2 \pi d \sin(\theta)}{\lambda}$, but it takes a little work to do that, and you need to know the details on how to work with this formula=it's a little tricky.

Edit: See https://www.physicsforums.com/insights/fundamentals-of-the-diffraction-grating-spectrometer/
for more details.

 

[Charles Link]

@Herculi Please see the "Edit" to post 3 above.