Aim
To
determine the wavelength, λ, of a Helium- Neon laser
Variable
Independent
variable: Number of order maximum, m
Dependent
variable: Sine of angular position, sin θ
Controlled
variable: distance between 2 slits, d
Background Theory of Diffraction Grating
A diffraction grating is
the tool of choice for separating the colors in incident light. The condition
for maximum intensity is the same as that for a double slit. However, angular
separation of the maxima is
generally much greater because the slit spacing is so small for a diffraction grating. In physic,
interference means that a phenomenon in which waves superpose to form a resultant
wave of greater, lower, or the same amplitude. Interference usually refers to the interaction of
waves that are correlated or coherent with each other, either because they come from the
same source or because they have the same or nearly the same frequency. When waves are going to cross or meet with each
other, the reaction between them called interference. Constructive interference
means the interference of two or more waves of equal frequency and phase,
resulting in their mutual reinforcement and producing a single amplitude equal
to the sum of the amplitudes of the individual waves. Destructive interference
means that the interference of two waves of equal frequency and opposite phase,
resulting in their cancellation where the negative displacement of one always
coincides with the positive displacement of the other.
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1 Helium-neon
laser
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2 Wooden block
·
1 retort stand
·
1 1000v step-down transformer
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1 diffraction grating
·
1 diffraction grating holder
·
3 metre ruler
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1 white board
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Procedure:
Figure 1: Set up of the experiment.
Figure 2: Top view of the Set-up of
the experiment with an A4 paper.
1.
Construct two tables, raw
data table and derived data table, to record the data.
2.
Place the helium-neon
laser on wooden blocks to make sure the level of the helium-neon laser is
parallel to the table.
3.
Connect the helium-neon
laser to the A.C power supply box.
4. Place a white board with
graph paper vertically at the opposite side of the helium-neon laser and place
two wooden blocks in front and back of the white board to support the white board
to make the white board perpendicular to the diffraction grating and parallel
to the edge of table.
5. Place the diffraction
grating holder with 100lines/mm diffraction grating between the helium-neon
laser and white board, make sure that the diffraction grating is 30cm away from
the white board.
6. Adjust the
100lines/mm diffraction grating to the same height level as the helium-neon
laser and make sure that the diffraction grating is directly in front of the
helium-neon laser.
7. Prepare an A4 paper
with a small hole with can let the helium-neon laser pass through then place it
at the head of the helium-neon laser.
8. Adjust the position
of the diffraction grating on the diffraction grating holder until the central
maximum laser beam reflected onto the A4 paper is directed into the helium-neon
laser.
9. Remove the A4 paper
from the helium-neon laser and cross mark the 7 spots which appear on the graph
paper on the white board with 2B pencil.
10. Turn off the
helium-neon laser source and put the white board flatly on the table.
11. Measure the distance
between the marked points at the order maximum.
12. Calculate the sine of the angular position, sin,
between the central maximum to the order maximums.
13. Record the results into the raw data table prepared
14. Calculate the sine of the angular position, sin,
between the central maximum to the order maximums.
15. Record the results into the derived data table
prepared.
16. Plot 2 graphs based on the data from both the raw and
derived tables.
17. Calculate the wavelength of the helium- neon laser
based on graph plotted using the data from the derived table.
Table of results
Raw data
Order maximum, m
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θ/o
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Distance between order
maximums / cm
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Average distance
between order maximum/ cm
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0
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1
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2
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3
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4
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5
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6
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7
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Derived data
Order maximum, m
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Sin θ/o
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Distance between order
maximums / cm
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Average distance
between order maximum/ cm
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0
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1
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2
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3
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4
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5
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6
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7
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Graph
Graph of raw data
Graph of derived data
Sample Calculation
Figure 4: Top view of experiment
set-up
Use the formula θ= tan-1(L/D) to calculate
the angular position, θ, between the central maximum to the order maximums.
D = distance between the diffraction grating and laser
spot of the central maximum on the white board (m).
L= average distance between order maximums in meters
which can be obtained by dividing the distance between order maximums by 2 as
the distance between the central maximum and any one of the same order maximum
on the left and the right side is always the same.
The
distance between the central maximum to the order maximum can be obtained when
calculating the average distance between order maximums.
Gradient of the graph of Sin θ against order maximum
should be calculated to find the wavelength of the helium-neon laser. Then, use
the formula m λ= d sin θ based on both the independent variable which is the
number of order maximum and dependent variable which is the sine of the angular
position, the equation of the straight line plotted on the graph is sin θ= 
m. sin θ is the
sine of the angular position, λ is the wavelength of the helium- neon laser in meters,
d is the distance between 2 slits out of the 100 slits used in meters and m is
the order maximum.
m. sin θ is the
sine of the angular position, λ is the wavelength of the helium- neon laser in meters,
d is the distance between 2 slits out of the 100 slits used in meters and m is
the order maximum.
According
to the equation sin θ= 
m,
m,
The
gradient of the Graph of Sin θ against order maximum = 
Hence,
λ
= the gradient of the Graph of Sin θ against order maximum x d
The value of d is constant
throughout the experiment as the type of diffraction grating does not change.
d= 
mm = 0.01mm=
1x10-5m
mm = 0.01mm=
1x10-5m
Therefore,
λ = the
gradient of the Graph of Sin θ against order maximum x (1x10-5m)
Discussion
Figure
above shows specular and diffuse reflection.
In
this experimental design, white board is used. The aim of projecting the
helium-neon laser beam onto a white board with a smooth surface is to ensure
that the laser beams undergo specular reflection as the figure shown above.
When the helium-neon laser beam pass through the diffraction grating so that
all of the 7 order maximums will be appeared on the white board therefore the
distance between order maximums measure will become more precise.
Specular
reflection means that the reflection of light rays from a surface when light
come from an incoming direction then it is reflected to an outgoing direction
as well. Also, in this experimental design white board is used, this is to
prevent a diffuse reflection because the white board is providing a smooth
surface. The laser beams diffracted from the diffraction grating will be
reflected in all directions as the figure shown above if a rough surface is
used in this experimental design. So that the order maximums will not appear on
the white board and the distance distance between order maximums measured will
be not precise.
Besides,
an A4 paper with a small hole at the centre is used in this experimental
design. This is to ensure that the laser beam would only pass through the hole
and not split into wrong directions.
There
are some strengths in this experimental design. First, the laser beam from the
helium-neon laser source is perpendicular to the diffraction grating. So that
the central maximum laser which emitted through the diffraction grating to the
white board is perpendicular to the slits of the diffraction grating. When it
is perpendicular to each other, the accuracy of the
distance between the order maximums obtained and the average distance between
order maximums calculated will increase. Hence, the accuracy of the sine of
angular position calculated and graph plotted will increase so that the
helium-neon laser calculated will be more accurate.
Other than that, diffraction grating holder is
used in this experimental design. The diffraction grating holder can hold the
diffraction grating stably to avoid it from shaking and changing of position of
diffraction grating. The platform of diffraction grating holder is adjustable
so that the position of diffraction grating can be adjusted to the best
position. This can make sure that the diffraction grating can be always
perpendicular to the laser beam emitted. Therefore, the accuracy of distance between the
order maximums obtained and the average distance between order maximums
calculated will increase. Also, the accuracy of the sine of angular position
calculated and graph plotted will increase so that it leads to a more accurate
wavelength of the helium-neon laser obtained.
Besides, another strength in this experimental design
is 100lines/mm diffraction grating is used. According to this experimental
design, 7 maxima are needed. If the diffraction grating used is 1200lines/mm,
the distance between maxima would be bigger so that 7 of the maxima would not
be on the graph paper of the white board, this causes that the maxima can be
marked.
There is a systematic error that might happen in
this experimental design. Firstly, the 100lines/mm diffraction grating used
might have some flaws or cracks on its slit which will causes some the the
incident ray from the laser sources that passes through the cracked diffraction
grating to be diffracted to somewhere else instead of on the white board. So
that the 7 order maximums and the average distance for all of the order maximum
may not be obtained which means the straight line on the graph might be shorter
and it may not pass through the origin. Hence, the calculated wavelength of the
helium-neon will not be accurate. To improve this error, experiment must make
sure that they check the the diffraction grating slit and make sure that it is
in a good condition and without any flaws present to increase the accuracy of
the calculation of wavelength of the helium-neon laser.
There are also some expected random errors that
might happen in this experiment design. First, the cross mark might not be
exactly in the centre of each maximum. When the cross marks are not in the centre
the distance between the order maximums obtained and the average distance
between the order maximums calculated to be not precise causing the sine of
angular position obtained to not be precise. The wavelength of
the helium-neon laser obtained from the gradient of the graph will be not
accurate because there may be scattered points on the graph plotted.
Moreover,
another expected random error is the variation of eye levels while observing
the laser spots formed on the white board. So that the distance between the order maximums
measured and the average distance between the order maximums calculated to be not
precise causing the sine of angular position obtained to not be precise. The
wavelength of the helium-neon laser obtained from the gradient of the graph
will be not accurate because there may be scattered points on the graph
plotted.
Safety precaution
There
are some precautions that we need to take note. Firstly, while conducting the
experiment do not try to look into the helium-neon laser beam to avoid it from
hurting your eyes, lens of human eyes will focus the beam of the helium-neon
laser spot on the retina even from a low-powered so that thermal damage might
happen to the retinal tissue. Secondly, be careful when moving the helium-neon
laser. Most of the helium-neon lasers are light and small enough to move it
easily, so when the experimenter wants to move the helium-neon laser during its
operation, be careful and make sure that the laser beam will not shine into
others eyes as the laser beam will hurt human eyes. Thirdly, make sure that an
operating laser is not unattended, when the laser is not in use turn in off to
avoid accidental exposure. Also, avoid touching the power supply to avoid
accidental explosion and causes injury.
