Diffraction Gratings
Paul Avery
Dept. of Physics
University of Florida
PHY 2049
Paul Avery
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Diffraction Gratings
Analysis similar to double slit
• Many slits instead of 2
• Slits still separated by distance d
• Maxima again occur only for d sin θ = mλ
• Maxima are much sharper
Example: N = 4 (first maxima shown below)
Grating
N=4
d
d
m=1
λ
2λ
d 3λ
d
4λ
θ
L
Waves
Path difference is exactly 1 wavelength between slits
As N increases, maxima occur at same location but sharper!
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Diffraction Gratings
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Diffraction Gratings
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Diffraction Gratings
Calculation of intensity
• Basically a product of single slit and multiple slit formula
• Let a = slit width, d = slit separation, N = # of slits
2
⎛ sin α ⎞ ⎛ sin β ⎞
I = I max ⎜
⎟ ⎜
⎟
⎝ α ⎠ ⎝ Nβ ⎠
α = π a sin θ / λ
β = N π d sin θ / λ
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Diffraction Gratings
Gratings in astronomy: “Spectroscopy”
• Use d sin θ = mλ to determine wavelength (θ measured)
• Typically have N = 60,000 – 100,000!!
• Sharp peaks allow closely spaced wavelengths to be resolved
x Important for distinguishing element “signatures”
x Find all the elements in a stellar spectrum
Example: Wavelengths at 600 and 600.05 nm
• Easily resolved with 60,000 slit grating
• Poorly resolved with 15,000 slit grating
• Too few slits ⇒ same location but lines too wide to tell apart
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Diffraction Gratings
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Diffraction Gratings
Example: High resolution solar spectrum near
sodium absorption lines
Note: 1 nm = 10 Angstroms
Sodium lines
λ D1 = 589.54 nm
λ D2 = 588.94 nm
Paul Avery
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Δλ = 0.60 nm
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Diffraction Gratings