# To determine the wavelength of LASER light using diffraction phenomena.

Aim: To determine the wavelength of LASER light using diffraction phenomena.

 Diagram For the Experiment
THEORY: Laser system uses very precise optics. Beam divergence is one characteristic
of a laser beam which indicates that how far a beam “spreads out” along its path. One
term used to describe this property is miliradians. One milliradian of beam divergence
means that the beam “spreads out” one millimeter for every 1000 millimeter of travel.
Note that the beam will have an initial beam diameter and that diameter will increase
over distance. This increase is known as beam divergence.
Another characteristic of the beam is called waist diameter. It is the beam’s minimum
size and the divergence happens from the waist diameter. It can be located anywhere with
respect to the laser but is often measured at the output window. There is a theoretical
minimum to the divergence of a beam with respect to the beam waist diameter. A laser
beam whose divergence approaches the minimum divergence is referred to as a Gaussian
beam.
The activity involves making very precise measurements of the beam diameter at the
laser head as well as at several points along the beam. The measurements involve the
amount of divergence of the beam from the source. Therefore, the original beam diameter
must be subtracted out of each subsequent measurement.

TheHe-Ne laser is the most widely used laser with continuous power output in the range
of a fraction of mW to tens of mW.
Helium atoms are first excited to the 2
1S and 23S metastable states in an electrical
discharge. The metastable atoms then collide with ground-state neon atoms, exciting
them to the 2s and 3s states, respectively. Three stimulated transitions are possible in
neon : 3s 3p (emitting at Î» ~ 3.39 Î¼m), 3s 2p (at Î» ~ 632.8 nm) and 2s 2p (Î» ~
1.15 Î¼m), the 3s2p transition gives the characteristic red laser light. (The 3.39 Î¼m
infrared radiation can be strongly absorbed by glass elements. ) The lasing action depends
on keeping the 2p and 3p states unpopulated. This is achieved by having a fast decay
route to the 1s state, which is relatively empty. The return to the ground state is achieved
via collisions with the walls of the discharge tube. The gas tube may have Brewster
windows inserted into the resonant cavity to plane-polarize the laser output, the cheaper
He-Ne lasers do nt. In the latter case the beam is randomly polarized.

Diode Laser:
This is a semiconductor laser. The population inversion is achieved by applying a voltage
across the p-n junction. In a normal p-n junction current flows across the junction due to
the combined effect of holes and electrons. In a laser diode, electrons recombine with the
holes and the excess energy is converted into photons (or light). These photons in turn,
interact with the successive incoming electrons and thereby produce more number of
photons. This sets up the stimulated emission. In traditional lasers the amplification of
light is achieved by pumping the emitted from atoms repeatedly between two mirror. The
analogous process in the case of diode laser happens when the photons bounce back and
forth in the p-n junction. The amplified light emerges out from the polished end.

Diffraction Grating: A plane diffraction grating consists of an optically plane glass
plate on which are ruled a number of equidistant, parallel straight lines. The lines divide
the glass plate into opacities and transparencies, the thickness of which is of the order of
the wavelength of visible light. The region where a lines is drawn becomes opaque
whereas the space between the two lines is transparent. The number of lines in a plane
transmission grating is of the order of 6000 lines per cm.
In laboratories an actual grating is not used as it is very costly. The original grating
usually ruled on a plate of speculum metal by a sharp diamond point fitted to a dividing
engine. For ordinary use replicas of the grating are obtained by depositing a very thin
film of gelatine on it. The film is removed when dry and is pasted on an optically plane
glass plate.
Its working principle is based on the phenomenon of diffraction. The space between lines
act as slits and these slits diffract the light waves there by producing a large number of
beams which interfere in such a way to produce spectra.

If a parallel beam of monochromatic light is incident normally on the face of a plane
transmission diffraction grating, bright diffraction maxima are observed on the other side
of the grating. These diffraction maxima satisfy the grating condition:
(a + b) X sinÎ¸n = nÎ»
Where (a + b) = the grating element =2.54/N, N being the number of rulings per inch of
the grating. Distance between two consecutive slits (lines) of a grating is called grating
element. If 'a' is the separation between two slits and 'b' is the width of a slit, then grating
element 'd' is given by;
d = a + b
Î¸n = the angle of diffraction of the
nth maximum
n = the order of spectrum which can take values 0, ±1, ±2, ±3 …….
Î»= the wavelength of the incident light
Clearly, the diffraction is symmetrical about
0 = 0. If the incident beam contains
different colors of light, there will be different
n corresponding to different in the
same order
n. By measuring n and knowing N, can be calculated.

Single Slit Diffraction: The phenomenon is similar to grating, only difference is that in
this case, only one slit is used instead of multi-slits in case of grating. Therefore, there is
some prominent changes in the fringe pattern. Please see the figure below. The central
bright spot is the central maximum followed by low intensity maxima which are called
secondary maxima.

Apparatus Required: He-Ne LASER, optical bench, slit, screen.

Observation for Grating Diffraction:

Number of lines on the diffraction grating = a = 300 per mm

N = a×10 = 3000 per cm

Grating element (a+b) = 1/N = (1/3) ×10-4 cm

Distance between grating and screen = r = 25.5 cm

 S.No. Order of Spectrum (n) Distance between Bright Spots (cm) Angle of Diffraction nÎ¸ =  (radian) Î¸ = × (degree) sinÎ¸ nÎ» = (a+b) sin Î¸ On one side (x1) On other side (x2) Mean x 1. For 1st order n = 1 5 5.1 5.05 0.1980 11.35 0.196 6.468×10-5 2. For 2nd order n = 2 10 10.5 10.25 0.4019 23.03 0.391 12.903×10-5

Calculations:

Therefore Î» = 6.468×10-5cm (For 1st order)

(For 2nd order) = 6.451×10-5cm

Mean Î» = 645.95 nm

Relative % error =  × 100 =  =-2.07%

Result:

By diffraction grating = Î» ± Î´Î» = 645.95 2.07%