Sean Chew
Fairview International School Subang
Experimental Report – Diffraction as a tool of
Metrology
Introduction
Diffraction is the slight bending of a wave (in this case, light) when it passes around the
edge of an object, with the amount of bending depending on the size of the opening. If the size of
the opening is larger than the wavelength of light, diffraction will not occur. If the size of the
opening is smaller than the wavelength of light, the diffraction will be quite noticeable. (University
of Illinois)
Experiment 1: Measuring the wavelength of light using a known grating
A diffraction grating is a filter that contains a large number of closely spaced slits used to
diffract any light that is passed through it, similar to that of a prism. By shining a light through it,
it is able to separate them into their maxima, thus creating a variety of dots where constructive
interference occurs.
To calculate the wavelength of light, the following equation can be used:
𝐷
𝑛
𝑠𝑖𝑛𝜑 = λ
Equation 1 – Wavelength equation
The formulated hypothesis of this experiment is “The wavelength of light can be measured
by filtering light through a diffraction grating, then acquiring the angle φ and the maxima order
n.” The constant variable is the intensity of the light used. The dependent (responding) variables
are the maxima order n and the angle φ which can produce an experimental value of the wavelength
of light. Assuming it is not given, the independent (manipulated) variable is the distance between
the diffraction grating and the screen.
Apparatus
The apparatus used during the conduction of this experiment were 1 CRADL∑ Slide
Holder, 1 CRADL∑ Screwdriver set, 1 White paper screen, 1 table lamp, 1 Diffraction grating of
500 lines/mm, 1 CRADL∑ Bias unit, 1 Rui Xiang Measuring tape, 1 pencil and 1 CRADL∑
Optical rail with a wooden board that has a hole in the center.
Method
Figure 1 - Experiment Setup
First, the CRADL∑ Slide holder was slid into the CRADL∑ Optical rail at an appropriate
distance from the wooden board, then screwed in to prevent movement by using the CRADL∑
Screwdriver set. After that, the diffraction grating was slit into the CRADL∑ Slide holder. Then,
the Rui Xiang Measuring tape was used to measure the distance between the slide holder and the
wooden board at the end of the optical rail. The white Paper Screen was then attached to the
wooden board with the hole on the white sheet was aligned with the hole in the wooden board.
This is to enable easy differentiation of colors in a later step of the experiment. Then, the table
lamp was placed behind the wooden board, and the light bulb positioned directly at the back of the
hole. The lamp was then switched on.
The diffraction grating was then looked through, and a visible series of colored dots was
seen. The colored dots represent the different orders, or maxima. At the green dots, the pencil was
used to mark their positions. The Rui Xiang Measuring tape was then used to measure the distance
between the marked spot and the hole in the center. All observations were recorded.
Results
Measurements
Distance between slide holder and screen: 39.6 cm ± 0.02
Distance between marked spots and hole: 11.0 cm ± 0.02
Using the above information, a diagram can be drawn:
Figure 2 – Trigonometry Diagram
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By using simple trigonometry, the angle φ between the hole and the green dot was calculated:
11.0 𝑐𝑚
Tan-1 39.6 𝑐𝑚
Φ
=φ
= 15.5o
By using the equation, the wavelength of light was calculated:
𝐷
𝑛
0,002 𝑚𝑚
3
𝑠𝑖𝑛𝜑 = λ
sin 15.5
-x4
1.78 × 10 mm
178 nm
=λ
=λ
=λ
Discussion
The theoretical value for the wavelength of light is between 400-700 nm. (NASA)
According to the results acquired from the experiment, the wavelength of light is 178 nm. This
falls outside the range of the wavelength of light. The percentage deviation from the theoretical
value (assuming it as 400nm) is 55.5%. It can be considered as an unreliable result, due to the fact
that it falls above the error margin 20%. Reasons for error could include human parallax error
when looking through the diffraction grating, or human error during measurement of distances and
lengths. The translucency of the ruler could have also affected the diffraction of the laser. If the
experiment was repeated, it is possible to get accurate results.
Conclusion
The formulated hypothesis of the experiment is “The wavelength of light can be measured
by filtering light through a diffraction grating, then acquiring the angle φ and the maxima order
n.” According to the results, the hypothesis is rejected, however it has a potential to be accepted
with more repetition of the experiment.
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Experiment 2: Measuring the wavelength of light using a ruler
A ruler has many 1mm markings on it. By slanting the ruler, the markings will appear to
be closer together (from a 2D point of view), but they are actually the same distance apart (from
a 3D point of view). Because light travels in a ray, though the 1mm gap is not big enough for it
to diffract slanting the ruler will cause the gap to appear to become smaller which thus allows
light to diffract.
The formulated hypothesis is “The wavelength of light can be calculated by measuring the
angle Φ by diffracting a laser through a ruler, as the markings can be adjusted to be smaller than
the wavelength of light.” The constant variable is the intensity of the laser light. The dependent
(responding) variable is the experimental value for the wavelength of light. The independent
(manipulated) variable is the distance between the ruler and the screen.
Apparatus
The apparatus used during the conduction of this experiment were 1 CRADL∑ Laser
Diode, 1 White paper screen, 1 CRADL∑ Bias Unit, 1 CRADL∑ Optical Rail, 1 Plastic Ruler, 1
Wooden Block, 1 CRADL∑ screwdriver set, 1 pencil, 1 Rui Xiang measuring tape and 1 piece of
Plasticine.
Method
Figure 3 – Experiment Setup
First, the white screen was attached to the wooden board on the optical rail. Then, the laser
diode was put on the rail, and screwed in. The bias unit was then connected to the laser diode.
After that, the measuring tape was used to measure the distance between the laser diode and the
white screen, and the value recorded. The plasticine was then stuck to the wooden block, and the
ruler stuck to the plasticine, as in the setup above. Then, the position of the ruler was adjusted until
the laser light could be seen diffracting. The measuring tape was then again used to measure the
distance of the part of the ruler where the laser light hit, D. The measurement was recorded. The
position of the first and zero orders were then marked, then the measuring tape was used to measure
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the distance between them and the hole in the middle of the wooden board. All observations were
recorded.
Results
Measurements:
Distance between laser diode and screen = 74.2 cm ± 0.02
Distance between ruler and hole = 60.8 cm ± 0.02
Distance between dot and hole = 8cm ± 0.02
D = 2cm
Φ = 7.50o
β = 3.43o
α = 4.07o
Δ = 6.03 x 10-3 mm
λ = 7.3 x 10-4
= 730 nm
Discussion
According to the results, the value for the wavelength of light is 730 nm. The theoretical
value of lambda is from 400-700 nm. Though the experimental value does not fall in the range of
the theoretical value, the value is very close to being in the range. If 700nm is used as the
benchmark, then the experimental value is only about 4% inaccurate from the theoretical value,
which indicates that the results are somewhat reliable. The most likely reason for the deviation
would most probably be human error during measurement as the error is so small. If the experiment
were repeated, the results would probably fall inside the experimental range.
Conclusion
The formulated hypothesis of the experiment is “The wavelength of light can be calculated
by measuring the angle Φ by diffracting a laser through a ruler, as the markings can be adjusted to
be smaller than the wavelength of light.” This has been proven to be true as diffraction was
observed when he laser light was projected through the markings of the ruler, which allowed Φ to
be calculated. Also, the wavelength of light was able to be measured and the result was close to
the range of the theoretical value. The hypothesis is accepted.
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Experiment 3 – Measuring the groove density of an optical storage disc
An optical storage disc (CD or DVD) has many tiny grooves, which is what allows data to
be stored in it. By reflecting a laser light beam off it, it is possible to measure the groove density
(spacing between each groove) of the optical storage disc. To calculate the groove density, the
following formula can be used:
DsinΦ = nλ.
Equation 2 – Groove Density Equation
The formulated hypothesis of this experiment is “Despite the distance between the optical
storage disc and the laser diode, the groove density can be calculated by reflecting a laser beam
off the optical disc and finding the distance between the first maxima dot and the hole.” The
constant variable is the intensity of the laser light. The dependent (responding) variable is the
distance between the dot and the hole. The independent (manipulated) variable is the distance
between the slide holder and the laser diode.
Apparatus
The apparatus used during the conduction of this experiment were 1 CRADL∑ Laser
Diode, 1 White paper screen, 1 CRADL∑ Bias Unit, 1 CRADL∑ Optical Rail, 1 CRADL∑
screwdriver set, 1 CRADL∑ Slide Holder, 1 Rui Xiang Measuring Tape, 1 pencil and a piece of
an optical storage disc.
Method
Figure 4 – Experiment Setup
First, the laser diode was put backwards on the rail and screwed into position. Then, the
slide holder was also screwed into position. The Rui Xiang Measuring tape was then used to
measure the distance between the screen and the slide holder. Then, the laser diode was attached
to the bias unit. The piece of optical storage disc was then placed inside the slide holder. Then, the
dot closest to the hole in the middle was marked on the white screen, and the measuring tape used
to measure the distance between the two. All observations were recorded.
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Results
Measurements
Distance between slide holder and screen: 20.5cm ± 0.02
Distance between dot and hole: 9.3cm ± 0.02
Using the lengths acquired, the following triangle was constructed:
Figure 5 – Trigonometric Diagram
Φ
9.3
= 𝑡𝑎𝑛−1 (20.5)
= 24.4
The following equation was then used to calculate the groove density D
D × sin φ
D × sin 74.4
D
=n×λ
= 1 × 7.3 x 10-4mm
=
7.3 ×10−4 𝑚𝑚
sin 74.4
= 7.58 × 10-4 mm
= 758 nm
Discussion
According to an online source, the theoretical value of the groove density (or track pitch)
of an optical storage DVD disc is 740 nm. According to the result acquired from the experiment,
the groove density of an optical storage DVD disc is 758 nm. The results seem to be quite close.
The percentage deviation from the theoretical value is only about 2.4%, which can be considered
acceptable because it is below the error margin 20%. Possible reasons for this small error
percentage could be human error when measuring any distances, or human error when positioning
the laser diode. As it is only a small error, human error seems to be the most likely cause. If the
experiment was repeated, the results could be much more accurate.
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Conclusion
The formulated hypothesis of the experiment is “Despite the distance between the optical
storage disc and the laser diode, the groove density can be calculated by reflecting a laser beam
off the optical disc and finding the distance between the first maxima dot and the hole.” The results
show that it is possible to measure the groove density of an optical disc by reflecting a laser beam
off it. Also, the experimental value is very close to the theoretical value. The hypothesis is
accepted.
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2.
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Works Cited
"Diffraction Grating." HyperPhysics. N.p., n.d. Web. 7 July 2014.
<http%253A%252F%252Fhyperphysics.phyastr.gsu.edu%252Fhbase%252Fphyopt%252Fgrating.html>.
Hofbauer, Wulf, Dr. Diffraction as a Metrology Tool. Singapore: CRADL∑ & Science
Center Singapore, 17 May. 2012. DOC.
NASA. "What Wavelength Goes With a Color?" NASA. NASA, n.d. Web. 7 July 2014.
<http%3A%2F%2Fscienceedu.larc.nasa.gov%2FEDDOCS%2FWavelengths_for_Colors.html>.
"Diffraction of Light: Light Bending around an Object." University of Illinois. N.p., n.d.
Web. 067July 2014.
<http://ww2010.atmos.uiuc.edu/%28Gh%29/guides/mtr/opt/mch/diff.rxml>.
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