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⎝ྎ d ⎠ྏ
−1 Small angle approximation
is not valid. λ1 ⎞ྏ
⎛ྎ λ2 ⎞ྏ
−1 ⎛ྎ
Δθ = sin ⎜ྎ m ⎟ྏ − sin ⎜ྎ m ⎟ྏ = 0.031°
⎝ྎ d ⎠ྏ
⎝ྎ d ⎠ྏ
−1 Lecture 4, p 17 Diffraction Gratings (1)
Diffraction gratings rely on Nslit interference.
They consist of a large number of evenly spaced parallel slits. An important question:
How effective are diffraction gratings at resolving light of different
wavelengths (i.e. separating closelyspaced ‘spectral lines’)?
IN = N2I1 λ1 sinθ depends on λ. 0 λ1/d sin θ λ2 0 λ2/d sin θ Example: Na has a spectrum with two yellow “lines” very
close together: λ1 = 589.0 nm, λ2 = 589.6 nm (Δλ = 0.6 nm)
Are these two lines distinguishable using a particular grating?
We need a “resolution criterion”. Lecture 4, p 18 Diffraction Gratings (2)
We use Rayleigh’s criterion:
The minimum wavelength separation we can resolve occurs
when the λ2 peak coincides with the first zero of the λ1 peak:
λ2/d λ1/d So, the Raleigh criterion is Δ(sinθ)min = λ/Nd.
However, the location of the peak is sinθ = mλ/d.
Thus, (Δλ...
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This note was uploaded on 03/27/2014 for the course PHYS 214 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 Quantum Physics, Diffraction

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