Determination of Single-Slit Diffraction and Double-Slit Interference Using Laser Diode as the Source of Light Canopio, Marco 1, Marco, Ardin 2, Sirot, icardo !" 1
Department of Geodetic Engineering, College of Engineering, Engineering, UP Diliman, Quezon City Department of Mechanical Engineering, College of Engineering, Engineering, UP Diliman, Quezon City 3 Department of Mining, Metallurgical and Material Engineering, College of Engineering, UP Diliman, Quezon City !correponding author" ra#$1%%&'yahoo(com 2
Abstract The experiment aims to study the interference and diffraction of light by investigating the patterns produced by single-slit and double-slit diffractio diffraction. n. The experiment experiment is divided divided into 3 parts- (1) investigati investigating ng the the patt patter ern n prod produc uced ed by diff diffra ract ctio ion n thro throug ugh h a sing single le slit slit and and determining its slit width, () investigating the pattern produced by diffraction through a double slit and calculating slit width, and (3) changing the slit width and slit separation of the diffraction produced from from a double double slit. The results results of the experime experiment nt contrib contribute uted d on understanding and studying the behavior of light.
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Introduction An RC circuit is a circuit composed of a power supply, a resistor and a capacitor. Capaci Capacito tors rs can store store electr electrica icall energy energy inside inside it when when charge charged, d, while while the resis resistor tor dissipates the energy to and from the resistor. In such circuits, it can be observed that the voltage, current and the power that ows through an RC circuit is not constant. The three quantities change with respect to time !". In the RC circuit, both the resistor and the capacitor are responsible for the time changing quantities. #hen connected to the power supply the capacitor will charge until it reaches its capacitance capacitance C. The charge in this capacitor will be equal equal to the product of the capacitance and the voltage of the power supply $". %&ee, 'qn %!(( )* )
As the capacitor+s charge goes to qo, its voltage V increases increases to ) while its potential di-erence across the resistor decreases ". This relation results to 'quation %$(.
% (* (* )%!// 0 ( #hen discharging, however, at time t*), the charge q is equal to 1) or the ma2imum charge inside the capacitor. 3rom 1), the charge decreases until ir approaches 4ero at time t , and at the same time, the voltage V, from 5) also approaces 4ero, thus resulting to 'qn %(
% (* (* )%/ 0 (
t is the time constant given by t *RC from a circuit with resistance R and Capacitance C 6"
The e2periment aims to quantify the rate of charging and discharging of a given capacitor that is in series with a resistor and power supply. 3rom it, e2perimental time constant could be measured and be compared with the theoretical time constant.
II# Methodolog$ The materials used in the e2periment were multimeter, !)))73 electrolytic capacitor, !)) 89 resistor, !) 89 resistor, connecting wires with clips, banana plug and stopwatch the e2periment was divided into parts, %i( resistance and capacitance measurements, %ii( charging RC Circuit and %iii( discharging RC Circuit. 3or the :rst part, a single slit dis8 was used. #ith a slit width of ).)6mm, a laser beam was centered on the slit. Then, the hori4ontal distance from the slit dis8 to the screen was determined. The lights were turned o- so that mar8ing the boundaries of the dar8 fringes the beam made on the white sheet will be easier and more accurate. The distance between the side orders and from center to side was then measured. The :rst part was repeated for a slit width of ).)$mm and ).);. 3or the second part of the e2periment, the power supply was set between <.) 5 and =.) 5. Two banana plugs were connected to the power supply with the red one for the positive terminal and the blac8 one for the negative terminal. >ne end of the resistor was connected to banana plug and the negative terminal of the capacitor was connected to blac8 banana plug. The capacitor was connected parallel to the voltmeter in ?C settings and with the 8nob set to $) 5. The power supply was turned on and the stopwatch was started as soon as the circuit was closed. The third part of the e2periment, one lead of the resistor was connected to one lead of the capacitor using alligator clips, li8ewise with the remaining free leads of both using another alligator clip. The terminals of the capacitor was connected to the corresponding terminal of the voltmeter in ?C settings and with the 8nob set at $) 5. The terminals of the capacitor was connected to the corresponding terminals of the power supply. The power was set between <.) 5 and =.) 5 and the power supply was turned on. The stopwatch was started as soon as the capacitor was disconnected to the power supply.
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Data and esults
The main purpose of the experiment was to demonstrate the interference and diffraction of light from a source passing through single-slit and double-slit with finite width !uantitatively and !ualitatively respectively. The source of light in this experiment was a laser diode with a theoretical wavelength of "#$ nm. A# esistance and Capacitance Measurements#
%n the first part of the experiment, the measurement of the resistance and capacitance value was performed. & multimeter was used in obtaining the measured value of the resistors and capacitor. The data gathered were listed in Table 1. Table 1.'esistance and apacitance easurements. *abelled +alue easured +alue 'esistor 1 !)) 89 !)),@ 89 'esistor !) 89 @.;! 89 apacitor 1 $.$3" !)))73
%# C Circuit &Charging'
%n the second part of the experiment, the ' circuit was charged. The capacitor in the ' circuit was charged and the increase of voltage was recoreded every # seconds. The data gathered were in Table .
Time (s) $ # 1$ 1# $ # 3$ 3# /$ /# #$ ## "$ "#
Table . +oltage vs. time data for ' charging +oltage across Time (s) +oltage across capacitor (+) capacitor (+) $.$ $ . $.3" # ./ $."3 $ 3.$ $.3 # 3.1 1.$" $ 3. 1. # 3./$ 1./ 1$$ 3./ 1.$ 1$# 3."1 1.$ 11$ 3.1 .$# 11# 3. .1 1$ 3. .3 .#3 .$
C# C Circuit &Discharging'
%n the third and last part of the experiment, the ' circuit was discharged. The charged capacitor in the previose step was used and the decrease of voltage was recorded every # seconds. The data obtained were recorded in Table 3. Table 3. +oltage vs. time data for ' discharging Time (s) +oltage across Time (s) +oltage across capacitor (+) capacitor (+) $ /.#$ $ ."# # /.3# # .#3 1$ /.1 $ ./ 1# /.$3 # .3 $ 3. $ .3 # 3." # .13 3$ 3."/ 1$$ .$# 3# 3.#1 1$# 1.# /$ 3.3 11$ 1. /# 3.# 11# 1.$ #$ 3.1 1$ 1. ## 3.$$ "$ . "# .#
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Conclusion and ecommendations
%t can be concluded that as the side order increases, the wavelength also decreases. &s it moves away from the central maximum, less light is encountered. The second part of the experiment yielded accurate results because of low percent errors obtained. 0urthermore, the third part of the experiment showed that as the slit width increases, the central maximum width decreases and as the slit separation increases, the width of interference fringes decreases. The experimental percent differences may have occurred from a number of possible errors. ne is the light coming from other sources that affects the propagation of light in the white screen. ¬her is the distance between the screen and laser. & greater distance resulted to dimmer and blurry diffraction patterns which made it difficult to measure. ther sources came from human errors. & dar2er environment to conduct the experiment is recommended.
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eferences
14 5ugh 6. 7oung, 'oger &. 0reedman, &. *ewis 0ord. Uni)erity Phyic *ith Modern Phyic( 3+, page 11-( .ddion/0elye, 13th Edition, 212 4 5ugh 6. 7oung, 'oger &. 0reedman, &. *ewis 0ord. 8niversity 9hysics with odern 9hysic. 3#, page 11"#. &ddison-:eslye, 13th ;dition, $1 346r. 'od
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http>??hyperphysics.phy-
/4 5ugh 6. 7oung, 'oger &. 0reedman, &. *ewis 0ord. 8niversity 9hysics with odern 9hysic. 3#, page 111. &ddison-:eslye, 13th ;dition, $1 #4 assachusetts %nstitute of Technology. B%nterference and 6iffraction=. hapter 1/, page 1. :eb. 'etrieved from http>??web.mit.edu?viC?;?visualiCations?coursenotes?modules?guide1/.pdf on # Aeptember $1#. "4 5ugh 6. 7oung, 'oger &. 0reedman, &. *ewis 0ord. 8niversity 9hysics with odern 9hysic. 3#, page 11. &ddison-:eslye, 13th ;dition, $1 4 ;xperiment > %nterference and 6iffraction (*ab manual). 9rinted 11 &ugust $1/.
