A diffraction grating is an arrangement of parallel, equally spaced lines that separates white light into its spectrum more effectively than a prism. Light passing through the grating will produce constructive interference at certain angles, called diffraction orders. For a grating with 600 lines per mm illuminated with yellow light of wavelength 6x10-7 m, the angles for zero, first, and second order diffraction can be calculated using the diffraction grating equation.

1. The Diffraction Grating

2. • A (transmission) diffraction grating is an
arrangement of identical, equally spaced
parallel lines ruled on glass.
• A typical diffraction grating will have
something like.600 lines per millimetre
600mm-1
Diffraction gratings
are used to produce
optical spectra

3. θ
d
C
A
B
Light of wavelength
λ, normal to the
grating Each of the clear spaces
(A,B,C etc) acts like a
very narrow slit and
produces its own
diffraction.
The light is from the same
monochromatic source
and therefore is coherent.

4. θ
θ
θ
d
C
A
B
Light of wavelength
λ, normal to the
grating
Consider the light which is
diffracted by each slit at
some angle θ to the
normal.
The slits are equally
spaced so that if angle θ
produces light that phase
at A and B (and therefore
positively reinforces )
then the light will also be
in phase from every
other slit and also
produce positive
reinforcement.

5. θ
θ
θ
d
C
A
B
Light of wavelength
λ, normal to the
grating
N
When the waves reinforce
each other the path
difference AN is a full
number of wavelengths .
That means that
AN =nλ
where n is a whole number
As:
AN = d sin θ
dsinθ = nλ

6. Diffraction Grating
• The angle θ will be slightly different for
each wavelength of light and so the
grating separates white light into its
spectrum and does this much more
effectively than a prism.
• The light needs to be focussed with the
eyepiece lens of a telescope or
spectrometer ( or the lens of the eye) after
it emerges from the grating.

7. The Diffraction Grating
• A diffraction grating with a large number of
lines produces very sharp maxima and
completely destructive interference at
other angles

8. Calculations
• A diffraction grating has 600 lines per mm. If such a
grating is illuminated with yellow light at 6 x 10-7 m,
calculate the angle at which zero, first and second order
diffraction will be observed
grating
zero order
diffraction
second order
diffraction
first order
diffraction
The diagram below shows the light passing through the grating.
zero order diffraction is always at 00 to the normal!

9. Calculations
• A diffraction grating has 600
lines per mm. If such a grating
is illuminated with yellow light
at 6 x 10-7 m, calculate the
angle at which zero, first and
second order diffraction will be
observed
Using nλ= dsinθ
The spacing of the
lines(d) is 1/600 000 mm
grating
zero order
diffraction
second order
diffraction
first order
diffraction
0
5
7
7
1
.
21
36
.
0
10
6
10
6
600000
1
10
6
1
sin
sin






















d
n
21.10

10. Calculations
• A diffraction grating has 600
lines per mm. If such a grating
is illuminated with yellow light
at 6 x 10-7 m, calculate the
angle at which zero, first and
second order diffraction will be
observed
Using nλ=dsinθ
The spacing of the
lines(d) is 1/600 000 mm
grating
zero order
diffraction
second order
diffraction
first order
diffraction
0
5
7
7
1
.
46
72
.
0
10
6
10
6
600000
1
10
6
2
sin
sin






















d
n
21.10
Try to calculate the angle
for 3rd order diffraction

11. Calculations
When a grating with 300 lines per mm is illuminated normally with a
parallel beam of monochromatic light a second order principle
maximum is observed at 18.90 to the straight through direction. Find
the wavelength of the light
300 lines per mm is 3.00 x 105 lines per metre and therefore the spacing
d =1/3.00 x 105m
A second order maximum means n=2
Using nλ= dsinθ
m
7
0
5
10
40
.
5
9
.
18
sin
10
00
.
3
2
1







