Parallel rays of a
monochromatic light of wavelength l
are incident on a diffraction grating in which the slit separation is d.
If the grating has N lines per
metre, the grating spacing is given by:
d = 1
N
Constructive interference only occurs along a few precise directions, one
of which is shown in the diagram. Light
from A must be in phase with light
from B, and this can only happen when
the path difference is a whole number
of complete wavelengths (even number of half-wavelengths).
AC = nl, where n = 0, 1, 2, 3...
Now:
AC = d sin q
where q is the angle of diffraction.
So it does not take a genius to see that:
d
sin q = nl
The term n is called the spectrum
order. If n = 1, we have the first
diffraction maximum.
Sin q can never be greater than 1, so there is a limit to the number of spectra that can be obtained.
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