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APEC Youth Scientist Journal Vol. 8, No. 2, August, 2016, pp. 31~36
http://www.sigs.or.kr
Wavelength verification of laser through varied slit widths
using a single slit diffraction set-up
*
Johanna G. Bantol1, *Rizelin John G. Ofelia1
1Philippine Science High School
– Central Visayas Campus, Talaytay, Argao, Cebu, PHILIPPINES
ABSTRACT: Being able to behave as a wave, light can be dispersed from its source point using
slit/s. This is called single slit diffraction. Using this ability, the wavelength of a certain light source,
like laser, can be determined. This is through the working equation:  
  =  . Through the
CCD (charge-coupled device), the diffraction of the light was seen and using the Vision Assistant
Program, the order for the destructive interference was known. The manipulated variable in this
research was the usage of different slit widths (0.04 mm, 0.08 mm, and 0.16 mm). It was seen from
the experiment that the wavelength is approximately close to the actual one. Even though different
slit widths were utilized in the study, the wavelength remained close to the original value. Data
analysis was done after the conduct of the study and it was concluded that the smaller the value of
the slit width, it became difficult to measure the value of the wavelength due to the larger distance
between the destructive interferences but it has a much more precise measurement, which was seen
in the calculations of the percentage error.
Keywords: single slit diffraction wavelength verification, laser, slit width
1. INTRODUCTION
Light behaves either as a wave or as a particle stated in the wave-particle duality. These particle and
wave properties of light have been resolved during the 1930’s through the progress of quantum
electrodynamics, which states the explanation of how light are both a wave and a particle (Crowell, 2003).
The wave model points out the propagation of light while the particle approach depicts its emission and
absorption (Young et al., 2012).
In this set-up, the light was seen to be a wave. The key to understanding why light behaves like waves
is through interference and diffraction. Both are the phenomena that distinguish waves from particles:
waves interfere and diffract while particles do not (Boston University, n.d.). Thus, the study is being
conducted in order to see how the light diffracts and with this diffraction, the wavelength can already be
known (Dyer, 2001). Moreover, the comparison of different slit widths enables the analysis of how the
wavelength may be affected by it.
Using the single slit diffraction set-up, one can determine the wavelength of the light source (laser)
given a fixed value for the slit width. The working equation behind this concept and the one utilized in the
study is:
*Correspondence
to : Johanna G. Bantol ([email protected]),
Rizelin John G. Ofelia ([email protected])
32 Johanna G. Bantol, Rizelin John G. Ofelia
 sin  =  
where:
a – slit width
 – angle between light ray to a point on the screen
m – order of the destructive interference
λ – wavelength of the laser
To determine the angle , the order m should be known. In our case, m=1 since this is mostly the
nearest place to the central maximum and is within the range of the CCD.
θ = tan


where:
y – distance from the center of the principal maximum to the center of
the first minimum (m=1)
L – length from the slit to the screen
In this paper, the main objective is to verify the wavelength and compare it through different slit widths,
which are 0.04 mm, 0.08 mm, and 0.16 mm. Specifically, it aims to: (i) use Vision Assistant Program and
CCD as an object for precision, (ii) calibrate the destructive interferences of the captured diffracted light
from the CCD, (iii) calculate the percentage error for each of the slit width, (iv) compare the data from
each of the slit width, and (v) graph the slope-intercept form of the data results through the working
equation.
2. MATERIALS AND METHODS
Materials:
Ÿ folder (150 mm x 215 mm)
Ÿ ruler
Ÿ laser (range: 630-680 nm)
Ÿ slit (width: 0.04, 0.08, and 0.16 mm)
Ÿ screen (paper with measurements attached with a lens paper)
Ÿ optical bench
Ÿ CCD connected to the computer
Ÿ Vision Assistant program
2.1 Calibration of the Diffracted Light
Calibration was first done through the simple use of a folder with a cut piece at the center. A paper with
measurements from 1 mm to 70 mm was placed on its center. This paper was then attached to a lens
paper and this whole part is already the screen. The set-up was prepared in an optical bench. The CCD
Wavelength verification of laser through varied slit widths using a single slit diffraction set-up 33
connected to a computer was placed near at the end of the bench, then, the screen, with 1 meter distance
to the slit, and finally the laser. Another calibration was also done for the camera by adjusting its focus so
that the lines of the measurements of the screen are seen. A picture was captured to verify precision of
results.
Figure 1. Experimental Set-up
Figure 2. Calibration of the screen
2.2 Diffraction Pattern Captured through CCD
Capturing the diffraction pattern, we first started with the biggest slit width which is 0.16 mm. We
turned on the laser and turned off the lights to be able to see the diffraction pattern clearly, adjusted the
camera’s focus to make the picture clear with its measurements and took the picture through the Assistant
Vision program. The same procedure was done for the 0.08 mm and 0.04 mm slits.
2.3 Verification of the Wavelength
The final part of the methodology is the verification of the wavelength. The variables should be known
in able to calculate the wavelength of the laser but the angle is still unknown. The angle was known

through the formula, θ = tan . However, only the variable L was known which is 1 meter. The

variable y was calculated using the different pictures captured. This is known by knowing the distance
from the center of the central maximum to the center of the first minimum which can be seen through the
picture for each slit width.
34 Johanna G. Bantol, Rizelin John G. Ofelia
3. RESULTS AND DISCUSSION
(a)
(b)
(c)
Figure 3. (a) 0.16 mm diffraction pattern with measurements,
(b) 0.08 mm diffraction pattern with measurements,
(c) 0.04 mm diffraction pattern with measurements
Table 1. Variable y for each slit widths
Slit Width (in mm)
y (in mm)
0.16
4.0
0.08
8.0
0.04
16.1
Sample calculation for the wavelength:
0.16 mm
θ = tan
4.0
≈ 0.229
1000
0.16 sin 0.229 ≈ 640 nm
Sample calculation for Percentage Error (using the mean 655 nm as the theoretical wavelength):
0.16 nm
|640 nm − 655 nm|
× 100% = 2.29%
655 nm
Here are the obtained percentage errors of the different slit widths:
Wavelength verification of laser through varied slit widths using a single slit diffraction set-up 35
Table 1. Percentage Error for the Slit Widths
Slit Width (in mm)
Error
0.16
2.29%
0.08
2.29%
0.04
1.68%
The results were gathered and analyzed to fit in a slope-intercept graph in Microsoft Excel. Using the
equation,  sin  =  , its slope intercept was placed into the variables x as

 
and y as  or slit
slit width (in mm)
width.
0.2
0.15
0.1
0.05
0
0
50
100
150
200
250
300
1/sinϴ (in mm)
Figure 4. Slope-intercept graph of the data results
As seen from the data being gathered, as the slit width decreased from 0.16 mm to 0.08 mm, no
significant change in percent error has occurred. However, as the slit size decreased from 0.08 mm to 0.04
mm, the percent error has been lessened, making a much more accurate measurement of the wavelength
of the laser. This shows that there is significance in its percentage error when the slit width is decreased.
The reason behind this is that, light is being diffracted in a wider way and there
4. CONCLUSION
The over-all set-up has been successful enough to gather the data necessitated. Calibration gave an
accurate measurement for the variable y in order to solve the wavelength of the laser. However, there is a
slight percentage error of the data which may be due to systematic error of the measuring equipments.
Moreover, the source of error can also be due to the place where the set-up was done since atmospheric
particles may disrupt the laser’s path and change the diffraction pattern on the screen. In the end, we were
still able to find a precise and reliable data for the single slit diffraction set-up.
36 Johanna G. Bantol, Rizelin John G. Ofelia
5. ACKNOWLEDGEMENTS
The researchers would like to thank the following: the University of San Carlos-Talamban Campus for
the support casted during the Science Internship Program of The PSHS-CVisC, especially to Dr.
Raymund Sarmiento of the Photonics Laboratory, Mr. Claude Cenizo, Mr. Dexter Manalili who were the
direct supervisors of the study; Mr. Benito A. Baje for his enthusiastic and unparalleled support to the
researchers in terms of encouragement and technicalities, not to mention his support as the researchers’
Physics 2 adviser and for being the wonderful AMGS mentor; Mr. Kyle A. De La Torre for all his
support in making the researchers achieve their goals, including lending his equipment; and of course, the
Almighty Father, for everything.
6. REFERENCES
[1] Boston University. (n.d.) Diffraction and Interference. Retrieved from, http://www.buphy.bu.edu/ulab/intro2/
diffraction.pdf
[2] Crowell, B. (2003). Optics. Edition 2.1., Book 5 of Light and Matter series.
[3] Department of Physics: Physics Lab. (2014). Interference and Diffraction of Light. Andrews University. Retrieved
from, http://www.andrews.edu/phys/wiki/PhysLab/doku.php?id=lab11
[4] Dyer, S. (2001). Survey of Instrumentation and Measurement. New York: John Wiley & Sons.
[5] Physics for Electrical Engineers. (n.d.). Single Slit Diffraction. National University of Singapore. Retrieved from,
http://www.physics.nus.edu.sg/sg_ephysics/documents/PC2232-Diffraction-revised.pdf
[6] Young, H., Freedman, R. (2012). Sears and Zemansky’s University Physics. 13th edition, 1089-1091.
Johanna G. Bantol
Rizelin John G. Ofelia