MCS260
CORNERSTONE 260 MONOCHROMATORS
68
19.2 THE GRATING EQUATION IN PRACTICE
When a parallel beam of monochromatic light is incident on a grating, the light is diffracted from the
grating in directions corresponding to m = -2, -1, 0, 1, 2, 3, etc. When a parallel beam of
polychromatic light is incident on a grating then the light is dispersed so that each wavelength
satisfies the grating equation. Positive orders have been eliminated from the illustration for clarity.
In most monochromators, the input slit and collimating mirror fix the direction of the input beam that
strikes the grating. The focusing mirror and exit slit fix the output direction. Only wavelengths that
satisfy the grating equation pass through the exit slit. The remainder of the light is scattered and
absorbed inside the monochromator. As the grating is rotated, the angles I and D change, although
the difference between them remains constant and is fixed by the geometry of the monochromator.
A more convenient form of the grating equation for use with monochromators is:
mλ = 2 x a x cos φ x sin θ
Where: φ = Half the included angle between the incident ray and the diffracted ray at the grating
θ = Grating angle relative to the zero order position
These terms are related to the incident angle I and diffracted angle D by:
I = θ + φ and D = θ - φ
Figure 40: The Grating Equation Satisfied for a Parallel Beam of Monochromatic Light
Figure 41: Polychromatic Light Diffracted From a Grating
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