90088262 MCS130B
CORNERSTONE 130B MONOCHROMATORS
68
17
16B
APPENDIX IV: GRATING PHYSICS TUTORIAL
17.1
61B
THE GRATING EQUATION
A typical diffraction grating consists of a substrate, usually of an “optical material”, with a large
number of parallel grooves ruled or replicated in its surface and overcoated with a reflecting
material such as aluminum. The quality and spacing of the grooves are crucial to the performanc e
of the grating, but the basic grating equation may be derived by supposing a sect ion t hrough t he
grating surface, normal to the ruling direction as a sawtooth pattern, shown below.
Light rays A and B, of wavelength λ, incident on adjacent grooves at angle I to the grating normal
are shown. Consider light at angle D to the grating normal; this light originat es from t he A and B
rays as they strike the grating. The path difference between the A1 and B1 rays can be seen to be:
a sin I + a sin D.
Summing of the rays A1 and B1 results in constructive interference if the path difference is equal t o
any integer multiple
of the wavelength λ:
a(sin l+ sin D) = mλ
Where m = an integer, and is the order of diffraction
This is the basic grating equation. Note that if D is on the opposite side of the grating normal from I,
it is of the opposite sign.
We have considered only two grooves. Including all the other grooves does not change t he basic
equation but sharpens the peak in the plot of diffracted intensity against angle D.
Figure 35: The Sawtooth Pattern of a Grating Section
Summary of Contents for Cornerstone 130B
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