Calculating the Number of Lines for a Diffraction Grating

AI Thread Summary
To determine the smallest number of lines needed for a diffraction grating to separate a doublet with a wavelength of 4,750˚A and a separation of 0.043˚A in the second order spectrum, the resolvance formula R = λ/Δλ = mN can be used. Substituting the values (λ = 4,750˚A, Δλ = 0.043˚A, m = 2) allows for solving N, the number of lines. The discussion also mentions the Rayleigh criterion and provides an alternative formula for intensity, which is more complex and requires a deeper understanding of diffraction principles. Additional resources are suggested for further clarification on the topic. Understanding these calculations is crucial for effectively using diffraction gratings in spectroscopy.
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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##.
 
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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.
 
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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.
 
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