Wavelength measurement through the use of a
diffraction grating
Task
To determine the wavelengths of light from the interference patterns produced by
passage of a narrow light beam through a diffraction grating. To identify the light
sources from their spectra.
Principle
Light or electromagnetic radiation may be viewed in one of two complementary ways:
as a wave of an electromagnetic field, or as a stream of massless particles called
photons. Occurrence of diffraction and interference is supporting evidence of the
wave nature of light, its particle behaviour you can encounter later when studying the
photoelectric effect. The range of wavelengths visible to human eye is about 380 nm
to 760 nm.
A diffraction grating is a set of many parallel slits used to disperse light employing
Fraunhofer diffraction. When light is incident on a diffraction grating, diffractive and
mutual interference effects occur, and light interferes constructively just in discrete
directions, depending on its wavelength. Therefore, a grating separates an incident
polychromatic beam into its constituent wavelength components, i.e., it is dispersive.
This is visually similar to the operation of a prism, although the mechanism is very
different. Diffraction gratings are often used in monochromators, spectrometers, etc.
Originally, high-resolution gratings were ruled to obtain fine parallel and equally
spaced grooves or rulings on material surface using high-quality ruling engines
whose construction was a large undertaking. Later, photolithographic techniques
allowed gratings to be created from a holographic interference pattern. Another
method for manufacturing diffraction gratings uses a photosensitive gel sandwiched
between two substrates. A holographic interference pattern exposes the gel which is
later developed, this yields a periodic modulation of the refractive index within the gel.
When a parallel coherent beam of light is incident
on a diffraction grating, each point of the slit emits
secondary wavelets in all directions, according to
Huygens' principle, which interfere to produce the
light and dark fringes on the screen. It can be
calculated that the light fringes appear in the
directions diffracted from the incident beam by the
angles k, satisfying the condition
(1)
  d sin k  k   , k  0,1, 2, ...
where  is the difference in optical path lengths
from the two neighbouring slits, d the distance of
the two adjacent slits, and λ the wavelength of the
light. The parameter k is called the order of a
maximum. The following identity holds:
Figure 1
sin k 
tan  k
1  tan 2 k
.
(2)
If bk is the distance of k-maximum from 0-maximum on the screen placed in the
distance a from the grating, it follows (see Fig. 3):
b
tg   k
a
(3)
Combining (1), (2), and (3) we finally obtain

bk d
b 
k  a 1  k 
 a 
2
d

 a 
k 1   
 bk 
2
(4)
Spectral lamps are filament-electrode gas discharge lamps with low internal pressure
As the light is emitted when an atom returns from its excited state to a lower excited
state or the ground state, the produced spectra are characteristic for a rare gas or a
metal vapour which the spectral lamps contains.
Figure 2
Equipment
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power supply for spectral lamps
spectral low-pressure lamps Cd, He, Na, Zn, and Hg, with housings
mercury high pressure lamp 80 W, lamp holder on stem
diffraction grating, 600 lines/mm on stem
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collimator
screen with line scale
free standing triangular optical rail, 1 m
rail carriers with holders, 4 pcs
measuring tape, 2 m
table of elements spectra
Set-up and procedure
The experimental set-up is as shown in Fig. 2 and 3.
Figure 3
1) Set up the experiment following the Fig. 3. L is the light source, C is the
collimator, G the diffraction grating, S the screen with a line scale. An optical
collimator consists of a tube containing a convex lens at one end and an
adjustable slit at the other, the slit being in the focal. It collimates a diverging
light beam from a point source to a parallel beam.
2) Switch on the lamp. The full intensity of the radiation will be obtained after a
few minutes of heating-up the lamp.
3) Set such a distance from the light source to the collimator to obtain intense
and narrow light strip in the middle of the grating.
4) Adjust the screen, measure the distance a and read the bk values (distances
of separate maxima from zero-maximum in the middle) for all the maxima
obtained. Fill them in the table. Use both the maxima on the left and right sides
of the screen, optionally repeat the measurement for several distances of the
screen a.
5) Calculate the wavelengths using the formula (4), for each spectral line (colour)
find the mean value of the wavelength and try to identify the source using the
table of elements spectra.
6) Repeat the whole measurement for at least one other light source.