How is the Angular Separation in a Diffraction Grating Calculated?

AI Thread Summary
The discussion focuses on calculating the angular separation in a diffraction grating with 3900 slits per centimeter for mercury's spectral lines at 579 nm and 577 nm. The angular separation is defined as the difference between the angles corresponding to these wavelengths, calculated using the equation d sin(theta) = m * lambda. A participant initially struggles with the calculations, mistakenly obtaining a sin(theta) value greater than 1, but later confirms their method is correct. For the second part of the problem, the Rayleigh criterion is suggested as a method to determine the necessary beam width for resolving the lines. Understanding the derivation of the equations is emphasized for accurate calculations.
WenyiJones
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Homework Statement


A diffraction grating of 3900 slits per centimeter is used to analyze the spectrum of mercury.
(a) Find the angular separation in the first-order spectrum of the two lines of wavelength 579 nm and 577 nm.
(b) How wide must the beam on the grating be for these lines to be resolved?


Homework Equations



dsin(theta)=m*lumda

The Attempt at a Solution



what is the angular separation? Is it just Theta?
 
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Yes, the angular separation is theta. You might want to read up on the derivation of the equation (if you haven't) so as to better understand it.
 
The way I read the question, angular separation would be the difference between the two angles (thetas) that you would calculate here.
 
the equation i used was:

maximum equation for multi-slit interference
d sin(theta)=m*lamda

d=distance between two slits
m=the interger called the order (bright spots)
theta=angular seperation
lamda=wavelength

but when i plugged in numbers, the sin(theta) i got was easily over 1, that is obviously wrong. what's wrong with it?
 
okay, the whole time i was calculating wrong.

it's correct!

how about (b)?
 
I should think it has to do with the Rayleigh criterion.
 

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