M77781A
MS257
™ USB/RS232
MONOCHROMATOR AND SPECTROGRAPH
61
Light rays
A
and B, of wavelength
I,
incident on adjacent grooves at angle
I
to the grating normal are
shown. Consider light at angle D to the grating normal; this light originates from the
A
and
B
rays as they
strike the grating. The path difference between the
A'
and
B'
rays can be seen to be a sinD + a sinl,
where a is the separation between neighboring grooves.
Summing of the rays A' and B' results in constructive interference only if the path difference is equal to a
multiple of the wavelength I :
a(sinl + sinD) = ml,
where
m
is an integer.
This is the basic grating equation, m is called the order of diffraction. Note that if
I
and
D
are on different
sides of the grating normal the sign of
D
is assumed to be negative.
We have considered only two grooves. Adding in the other grooves does not change the basic equation
but sharpens the peak in the plot of diffracted intensity against angle
D
.
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. This is shown in Figure 23, and discussed
further under "Grating Orders" in Appendix A.
Figure 23: The "Grating Equation"
In monochromators designed by Oriel Instruments, the input slit and collimating mirror fix the direction of
the input beam that strikes the grating. The output collimating mirror and slit fix the angle
D
, as they
determine the direction that light from the grating must go to exit the monochromator. Only wavelengths
which 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. The
wavelength I changes as the grating angle changes and:
λ=2*(a*cos
θ/2)*sinφ
where
θ is the angle between the incident ray and the diffracted ray at the grating, and φ is the grating
angle relative to the zero order position.