The diffraction grating (a thin film with hundreds or thousands of tiny parallel lines) produces interference patterns (Young's Experiment) with very sharp, bright fringes compared to a double-slit apparatus.
This is because each fringe produced by a grating is a result of the superposition of light from hundreds of lines.
The first-order fringe is produced when the path difference for light coming from adjacent lines is one wavelength.
The second-order when the path difference is two wavelengths, and so-on.
de=2λ
fg=3λ.
If it shows the 2nd-order, then:
bc=2λ
de=4λ
fg=6λ.
The angle of the n-order fringe can still be found using nλ=dsinθ, or the approximation nλ=dx/L
Young's type interference can also be seen with CD's, in which the pits act like the lines of the diffraction grating. The photograph on the left shows incident laser light (strong vertical beam) striking a CD and producing antinodal lines. The zero, first and second-order lines can be seen very clearly.If light of λ=632nm is incident on a CD, and the distance between the two first-order fringes is 98.4cm on a screen 1.20m from the CD, what is the distance between pits?
Link to Hyperphysics
Link to Diffraction Grating Applet
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Homework solution:
Halving the distance between the first-order fringes gives x=0.492m.
The angle of the first order is therefore found from tanθ=0.492/1.20
Therefore θ=22.3°
nλ=dsinθ
n=1
λ=6.32E-7
sinθ=0.379
d=nλ/sinθ
d=1.67E-6m (1.67μm)
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