How is the Angular Separation in a Diffraction Grating Calculated?

Click For Summary

Homework Help Overview

The discussion revolves around calculating the angular separation in a diffraction grating setup, specifically analyzing the spectrum of mercury with two closely spaced wavelengths. The problem involves understanding the relationship between the grating's properties and the resulting angular measurements.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of angular separation and its calculation, questioning whether it refers to a single angle or the difference between two angles. There is also exploration of the relevant equations and their application to the problem.

Discussion Status

The conversation includes attempts to clarify the concept of angular separation, with some participants suggesting the need for a deeper understanding of the underlying equations. There is acknowledgment of calculation errors and a shift in focus to the second part of the problem regarding beam width and resolution.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The discussion reflects uncertainty regarding the application of the diffraction grating formula and the implications of the Rayleigh criterion for resolution.

WenyiJones
Messages
4
Reaction score
0

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?
 
Physics news on Phys.org
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 separation
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.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
6
Views
3K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
10
Views
3K
  • · Replies 3 ·
Replies
3
Views
5K
  • · Replies 2 ·
Replies
2
Views
5K
  • · Replies 8 ·
Replies
8
Views
27K