Double Slit Experiment
Aims
The aim of this experiment is to investigate the double-slit interference of light. In addition, this experiment aims to show that little particles of matter are able to affect the wave behavior. This experiment therefore helps us in understanding the language of dimensional waves through the phenomenon of diffraction and interference. This experiment will use the two dimensional waves to achieve the aim of the experiment.
Introduction
When the length of the waves is much longer than the widths, it is important to treat them in two dimensional ways in order to understand their characteristics. This helps to reduce the diffraction of the wave while reducing the complexity of understanding the wave. The use of the Huygens’ principle is important in overcoming the major difficulties of slit in experiment (Rosa, 2012). When classical particles are ablaze in a straight line and through a slit, then they are able to strike screen the other side, the particles to reflect both the size and the shape of the slit. G. I. Taylor in 1909 was able to develop the first low intensity double slit experiment (Baggott, 2011 and Bush, 2010). This was achieved by reducing the level of i9ncident light up to when the photon emission or absorption were non-overlapping. The experiment kept on using light without anything else until 1961, when Claus Johnson was able to perform it with electron beam (Cassidy, 2008). Later, developments were made and the experiment was carried out using single electron and bisprism instead of slit. This helped to show that electrons interferes with itself as it is indicated in the quantum theory.
Developments continued later when the single-electron version of the experiment was created and voted the utmost beautiful experiment (Bush, 2015). In this experiment, particles are send from side to side the double slit experiment apparatus and the results are able to show that single particles are able to appear on the screen. The interference pattern is able to show that these particles build one by one. This experiment has been able to show that the electrons, photons, atoms and some key molecules are able to have the same properties. Moreover, the double slit experiment is able to show that the waves are modeled in a classical wave theory. This model is able to state that “each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point” (Plotnitsky, 2012). The phase and amplitude of the wave are the important parameters which are able to take the summation needs. In addition, the intensity of the wave can be found through this experiment. Studies have shown that the intensity of the wave has direct relation to the amplitude squared.
In this experiment, the double slits are usually lit up by a laser beam of light. Different sizes of the slits are able to be used. When the slit width is much small than the laser light wavelength, the slits are able to spread the light into cylinder-shaped waves (Couder, & Fort, 2012). Moreover, when carried out, the distance between the two waves is determined by the differences in phases of the two waves. When performed, the two cylindrical wavefronts are usually superimposed as well as their amplitude. Due to the superimposition, the intensity of the wave at any point of the combined wavefronts is able to depend on the phase and magnitude which the two wavefronts are able to possess (Quznetsov, 2011). Moreover, the differences in the phases for the wavefronts which is amid the waves and it is dogged by the dissimilarity in the distances which is available between the waves. The path difference which is flanked by the waves at any angle θ, is represented by;
dsinθ= dθ; d = distance between slits
In addition, when the path difference for the wavefronts is “equal to an integral number of the wavelengths, the sum of the amplitudes and the sum of the intensity is maximum” (Lederman, & Christopher, 2011). The path difference which arises at this situation is usually equal to 0.5, 1.5, 2.5, 3.5…. wavelengths. At this situation, the two waves are able to cancel out and the sum of the intensities is equal to zero. This situation is usually known as the interference (Bach, 2013). Different wavefronts are able to result to the same situation regardless of their states.
APPARATUS
- Optical bench, Projection screen
- Red and Green laser pointer.
- Ruler, Laser mount and Slide mount
- Glass microscope slides.
- Candle and matches.
- Razor blades and binder clip.
- Enameled wire.
- Wire cutters.
- Cellophane tape.
PROCEDURE
- First, prepare the pair of slits by collecting the thin film of carbons black on the part of microscope and slide on the orange part.
- Measure the double slit interference pattern using the red laser.
- Next measure the wire thickness and count number of turns present.
- Using the green laser, measure the wavelength used to observe the double slit interference.
- Using the green laser, also measure the slit spacing
- Lastly use the red laser to measure the wavelength of the waves.
RESULTS:
b (mm) | Larger Minima (cm) | θ bigger | b bigger | M | m-0.5 |
Average θ | 2 | 0.012903 | 0.041233 | 1 | 0.5 |
0.003212919 | 2 | 1.5 | |||
0.008514323 | 3 | 2.5 | |||
0.014297951 | 4 | 3.5 | |||
0.019760702 | 5 | 4.5 | |||
0.025706136 | 6 | 5.5 | |||
0.030527418 | 7 | 6.5 | |||
0.035831649 | 8 | 7.5 | |||
0.038886048 | 9 | 8.5 | |||
0.041458457 | 10 | 9.5 |
Average θ | Larger Minima (cm) | θ bigger | b bigger | M | m-0.5 |
0.001606457 | 2 | 0.012903 | 0.041233 | 1 | 0.5 |
0.004176799 | 2 | 1.5 | |||
0.006747169 | 3 | 2.5 | |||
0.009478236 | 4 | 3.5 | |||
0.013976627 | 5 | 4.5 | |||
0.017993285 | 6 | 5.5 | |||
0.020403414 | 7 | 6.5 | |||
0.023295728 | 8 | 7.5 | |||
0.027473864 | 9 | 8.5 | |||
0.031491754 | 10 | 9.5 |
Average θ | Larger Minima (cm) | θ bigger | b bigger | M | m-0.5 |
0.000645161 | 2.1 | 0.013548 | 0.03927 | 1 | 0.5 |
0.002741929 | 2 | 1.5 | |||
0.004516098 | 3 | 2.5 | |||
0.006451523 | 4 | 3.5 | |||
0.008225621 | 5 | 4.5 | |||
0.009999667 | 6 | 5.5 | |||
0.011773649 | 7 | 6.5 | |||
0.013708818 | 8 | 7.5 | |||
0.015643885 | 9 | 8.5 | |||
0.017095109 | 10 | 9.5 |
DISCUSSION
From the view of the graphs, it is clear that the differences in the average θ is able to lead to the same change on the graph. The maxima are able to have the same change and the slope of the graphs are the same for all the graphs. The analysis of the graphs is able to show that regardless of the angle or the size of the particles, the result of the maxima of the wavelengths is able to show that the interference situations is able to happen in every wave which is carried out in this experiment. The line graphs are positive and have close to the same level of the gradient. This is able to prove that the waves are able to behave the same way regardless of the differences of the particles used.
CONCLUSION
In conclusion, the waves from photons, electrons and other particles are able to have the same behavior. The double slit experiment is able to show that the wave behavior is the same regardless of their differences. Huygens–Fresnel principle is able to explain the behavior of the waves through the slit. Through the experiment, different waves characteristics can be found. Characteristics such as the wavelengths, the intensity and amplitude are able to define the characteristics of the waves. The wavelength interferences are all the same for all waves regardless of the differences in the characterizes of the specific waves.
REFERENCES
Bach, R.; (March, 2013). “Controlled double-slit electron diffraction”. New Journal of Physics. 15 (3): 033018.
Baggott, J. (2011). The Quantum Story: A History in 40 Moments. New York: Oxford University Press. pp. 76.
Bush, J. W. M (2015). “Pilot-wave hydrodynamics” (PDF). Annual Review of Fluid Mechanics. 47: 269–292.
Bush, J.W. M. (2010). “Quantum mechanics writ large”. PNAS. 107 (41): 17455–17456.
Cassidy, D. (2008). “Quantum Mechanics 1925–1927: Triumph of the Copenhagen Interpretation”. Werner Heisenberg. American Institute of Physics.
Couder, Y. & Fort, E. (2012). “Probabilities and trajectories in a classical wave-particle duality” (PDF). Journal of Physics: Conference Series. 361: 012001.
Lederman, L. M.; & Christopher T. H. (2011). Quantum Physics for Poets. US: Prometheus Books. pp. 102–111.
Plotnitsky, A. (2012). Niels Bohr and Complementarity: An Introduction. US: Springer. pp. 75–76.
Quznetsov, G. (2011). Final Book on Fundamental Theoretical Physics. American Research Press.
Rosa, R (2012). “The Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment”. Physics in Perspective. 14 (2): 178–194.
Laboratory Manual
LABORATORY SAFETY RULES
- Evacuation of Science Building
1.1 The building is to be evacuated whenever there is a fire or when a substantial spill of noxious or hazardous chemicals has occurred.
Evacuations will proceed when | A. The fire alarm is sounded | |
B. “House” warning systems are operated. | ||
1.2 | The Senior Demonstrator or Supervisor will organise the evacuation of the class or | |
group. | ||
1.3 | Students will evacuate in an orderly manner using the “buddy” system, ie in pairs, each | |
member of a pair being responsible for the other. | ||
1.4 | Undergraduate students are to assemble outside Science II (N34). | |
1.5 | A head count will be carried out by the supervisor. |
Eye Protection
2.1 Safety glasses are to be worn when directed.
2.2 The usage of contact lenses should be reported to the demonstrator.
2.3 Eye injuries from chemical splash, should be irrigated immediately with copious quantities of clean water and reported to the demonstrator immediately.
- Laboratory Coats Laboratory coats must be worn when directed in the laboratory.
- Footwear Open sandals, thongs or bare feet will not be permitted in laboratories or Shoes must be worn in these areas.
- Eating and Drinking in Laboratories
For the obvious reasons of personal safety and hygiene, eating and drinking in laboratories is not permitted. The common room is the only designated eating area in the building. Chewing gum is not permitted in the laboratory.
- Smoking is not permitted in any University building.
- Accidents All accidents must be reported to the demonstrator in charge and an accident report form filled out. This includes glassware, electrical fusion and chemical spills.
- Running in the Building
Except in a dire emergency running will not be permitted in the building.
- Fire Extinguishers, Hoses, Alarms or other Warning Systems
Are not to be misused, and in an emergency they will need to be in first class condition. You should identify all safety features in the laboratory (such as safety showers, exits, fire extinguishers and fire blankets).
- Transistor Radios and Cassette Players are banned from all laboratories.
- Broken Glass
For safety sake do not use broken or damaged glassware. Do not put broken glassware in normal rubbish bins; it is to be placed in the yellow bins provided.
1032SCG Physics 1b
1.2 GREEK ALPHABET | |||||
A, a | alpha | I, i | iota | P, r | rho |
B, b | beta | K, k | kappa | S, s | sigma |
G, g | gamma | L, l | lambda | T, t | tau |
D, d | delta | M, m | mu | U, u | upsilon |
E, e | epsilon | N, n | nu | F, f | phi |
Z, z | zeta | X, x | xi | X, c | chi |
H, h | eta | O, o | omicron | Y, y | psi |
Q, q | theta | P, p | pi | W, w | omega |
1.3 PHYSICAL CONSTANTS
Avogadro’s No. | N | 6.0222 x 10^{23} mol^{-1} |
A | ||
Boltzmanns Constant | k | 1.381 x 10^{-23} J K^{-1} |
Electron rest mass | m_{c} | 9.110 x 10^{-31} kg |
Gas Constant | R | 8.314 JK^{-1} mol^{-1} |
Permeability of a vacuum | ^{m}0 | 4 p x 10^{-7} H m^{-1} |
Permittivity of a vacuum | e | 8.854 x 10^{-12} F m^{-1} |
0 | ||
Plank’s Constant | h | 6.626 x 10^{-34} J s |
Proton rest mass | m_{p} | 1.673 x 10^{-27} kg |
Speed of Light | c | 2.998 x 10^{8} m s^{-1} |
Electron Charge | e | 1.602 x 10^{-19} C |
Standard Gravitational | g | 9.80665 m s^{-2} |
Acceleration | ||
Atmospheric Pressure | 1 atm = 1.01325 x 10^{5} N m^{-2} = 760 mm Hg |
1.4 AUSTRALIAN STANDARD SI UNITS
Quantity | Name of Unit | SI Symbol |
length | metre | m |
mass | kilogram | kg |
time | second | s |
electric current | ampere | A |
temperature | kelvin | K |
luminous intensity | candela | Cd |
amount of substance | mole | mol |
plane angle | radian | rad |
solid angle | steradian | sr |
volume | cubic metre | m^{3} |
1032SCG Physics 1b
1.5 DATA MANIPULATION
1.5.1 ERROR ANALYSIS
In these laboratories you will be expected to estimate the uncertainty or error in all of your results. This means that you must estimate how well each measurement can be made and use the following error rules to determine the error in any ensuing calculations to determine the error in your final results. This will appear to be a chore initially but with practice the task will not be too difficult or time-consuming in most cases, especially if the principles found at the end of this page are followed.
- Mean and error of repeated readings:
If you have repeated readings of an experimental value x_{1}, x_{2} .. x_{n} , then the mean value is
= | x_{1} +x_{2} +…+x_{n} | (1) | |||||||
x | |||||||||
n | |||||||||
S | |||||||||
and the best estimate of the error in the mean is S_{m} = | |||||||||
( | n -1 | ||||||||
) |
where S, the sample standard deviation is given by:
é | x | – | 2 | + | x | – | 2 | + …. + | x | – | 2 | ù | |||||||
1 | x | x | x | ||||||||||||||||
( | ) | ( _{2} | ) | ( _{n} | ) | ||||||||||||||
S = ê | n | ú | (2) | ||||||||||||||||
ë ê | û ú | ||||||||||||||||||
Therefore the best estimate of the value is x ± S_{m}
- Combination of errors:
Suppose two physical quantities are measured, and their magnitudes are A and B. Suppose the error in A is ∆A, and the error in B is ∆B.
Then if z = A + B or z = A – B
the error in z is | Dz = | ( | + DB^{2} | ) | (3) | |||||||||||
DA^{2} | ||||||||||||||||
Also if | z = AB | or | z = A/B | |||||||||||||
the error in z can be calculated from the following expression | ||||||||||||||||
DZ | é | 2 | 2 | ù | ||||||||||||
= | æ DAö | + | æ DBö | (4) | ||||||||||||
Z | ê è | A | ø | è | B | ø | ú | |||||||||
ë | û |
It should be noted that equations (3) and (4) can contain any number of terms inside the brackets and it is common to find that one or two of the terms dominate the expression. If this is the case then all other terms can be ignored.
1032SCG Physics 1b
- General expression:
On many occasions the quantity you want to calculate will be a more complicated function of the measured values. To see what we need to do in these cases, imagine that you want to estimate the error in a quantity F which is a function of the measured values x and y, i.e. you want to estimate the error in F ( x, y) when you know the errors Dx and Dy in the measured values x and y . The way to
think about this problem is to first think what would happen to the value of F if x increases by a small amount, say d x . From the small change (or small increment) formula we know that the change to F is approximately
¶F ( x , y) _{d} _{x} _{.}
¶x
Similarly, the change to F if y increases by a small amount, say d y is
¶F ( x , y) _{d} _{y} _{.}
¶y
We could use these formulas with d x = Dx and d y = Dy , and then somehow combine them to get an estimate of the total change in F. But we don’t know if the errors Dx and Dy are increases or
decreases in x and y and so we need to account for both possibilities. It turns out from a statistical analysis of all possible situations that the best estimate of the error in F under these circumstances is given by taking the square root of the sum of the squares of the two estimates like this:
æ ¶F ( x , y ) | _{ö}2 | æ | ¶F ( x , y) | ö^{2} | ||||
DF ( x, y ) = | ç | Dx _{÷} | + _{ç} | Dy _{÷} . | (5) | |||
¶x | ¶y | |||||||
è | ø | è | ø |
If F depends on three variables x, y, and z, then the formula is easily extended to
æ ¶F ( x , y , z ) | ö ^{2} | æ | ¶F ( x, y , | |||
DF ( x, y , z ) = | ç | Dx _{÷} | ^{+ }ç | |||
¶x | ¶y | |||||
è | ø | è |
z ) | _{ö}2 | æ ¶F ( x, y , | |
Dy _{÷} | ^{+ }ç | ¶z | |
ø | è |
and so on. In the case where F depends on a single variables x, the formula simplifies to
¶F ( x, y) | ||||
DF ( x ) = | Dx | . | ||
¶x | ||||
Exercises:
- Show that the formula (5) for the case where F ( A, B) = A + B gives the same result as expression (3).
- Evaluate formula (5) for the case where F ( A, B) = A ´ B . Divide your answer by F and show that it reduces to the expression (4).
- Let F ( a, b) = a ln b . Use formula (5) to estimate the error in F due to errors in measurements
of a and b. You should find that
DF = (ln b . Da )^{2} + _{ç}^{æ} | a | _{D}_{b}_{ ÷}ö^{2} | . |
è b | ø |
Show that, on dividing both sides by F, the relative error in F is
DF | æ | Da ö ^{2} | æ | Db ö^{2} | |||
= | ç | ÷ | + _{ç} | ÷ ^{.} | |||
F | |||||||
è | b ø | è b ln b ø |
When doing error estimation remember the following principles.
- Record the raw error data when recording a measurement.
- Calculate the error in your result only after you have calculated the final result.
- Remember that the value and its error should have the same units.
1032SCG Physics 1b
1.5.2 SIGNIFICANT FIGURES
- To ascertain the number of significant figures in a value, write it in scientific notation and count the number of digits present.
eg. | 0.000671 | 6.71 x 10^{-4} | 3 sig. fig. |
0.263 | 2.63 x 10^{-1} | 3 sig. fig. | |
0.01230 | 1.230 x 10^{-2} | 4 sig. fig. |
Zeros on the right of a digit usually mean that they are significant. This should be substantiated by the quoted error eg 26.100 ± 0.005 has 5 significant figures but 1000 ± 50 has only 3 significant figures.
- When doing calculations the number of significant figures in the answer should be equal to the lowest number of significant figures in any of the values used for the calculations.
eg (a) 16.375 x 21.6 x 5.0 x 17.35 = 30683
this answer should be quoted as 3.1 x 10^{4} or 31000.
- 226715 x 0.0012163 = 0.0002757535 this answer should be quoted as 2.7575 x 10^{-4}.
- Errors are only quoted as one significant figure. When calculating this figure, the number should always be rounded UP at the end of the calculation. This is only true for errors, as the error quoted should represent the largest possible value of the error range.
eg (a) | ∆Z | = | ± 0.00131 | then ∆Z = | ± 0.002 | |
(b) | ∆Z = ± 1.023 | then | ∆Z = | ± 2 | ||
(c) | ∆Z | = | ± 1.51 | then | ∆Z = | ± 2 |
- Pure numbers: Some formula such as 2pr etc involve pure numbers.
ie there is no inaccuracy in the number ‘2’. Thus the integer ‘2’ implies 2.000000000………. and therefore does not restrict the number of significant figures in the final result.
- Always check that your answer and its error are sensible. The answer should be rounded OFF, according to the significance of the error.
eg (a) | 21.3 ± 0.5 | = 3.17 ± ∆Zwhere ∆Z = 0.0781 ≈ 0.08 | |
6.71 ± 0.05 | |||
therefore the answer should be quoted as 3.17 ± 0.08 | |||
(b) | 21 ± 9 | = 3.0 ± ∆Zwhere ∆Z = 1.3 ≈ 2 | |
6.9 ± 0.9 | |||
therefore the answer should be quoted as 3 ± 2 |
1032SCG Physics 1b
1.5.3 UNIT ANALYSIS
The two sides of a mathematical equation must be equal, both in the numerical value and the units. A mathematical expression that gives a numerical answer must also work for the units of the variables it contains. Therefore, checking the units on both sides of an equation is a good way to check whether or not the equation makes sense. If the units on both sides of the equal sign differ then something is certainly wrong with the equation. Of course, the equation could still have a problem if the units balance correctly.
The method:
- Assign units to all variables on both sides of the equation.
- Break the variables up into a common set of (preferably) SI units (m, kg, s, etc.).
- Rearrange the units of both sides using standard algebra to get (hopefully) the same form.
- Compare the two sides of the equation.
EXAMPLE
The kinetic energy of a moving body can be written
K . E. = | p ^{2} | ||
2 m | |||
where | p is momentum | ||
m is mass |
LHS units: K.E. is an energy with unit joule (J)
1 J = 1 N.m (work is energy and work = force ´ distance)
newton (N) is the unit of force and
force = mass ´ acceleration, so
- N = 1 kg.ms^{-2}
- J = 1 kg.m.s^{-2}.m
- 1 kg.m^{2}.s^{-2}
RHS units: momentum = mass ´ velocity with unit kg.m.s^{-1}. Now drop the “1” for convenience.
_{RHS} _{=} (kg.m.s^{–}^{1})^{2}
kg
- kg^{2}.m^{2}.s^{-2}.kg^{-1}
- m^{2}.s^{-2}
- LHS
1032SCG Physics 1b
1.5.4 PLOTTING GRAPHS
When plotting graphs you should follow these rules:
- Determine which variables belong on which axis from the experimental information ie. X axis – independent variable
Y axis – dependent variable
The independent variable is the one which is changed by the experimenter.
The dependent variable is the one which measures the effect of changing the independent variable.
- Label the axis with the variable name and its units.
- Scale the axis to convenient numbers that make the total graph area cover approximately 80 – 100% of the piece of graph paper. The scale should reflect the errors in calculations made from reading the graph. NB the origin does not necessarily appear on every graph.
- The graph must have a title and a number
- “Graph 1 : The Dependence of the Solubility of MX on Temperature”
“Figure 1 : The Absorbance of X at 560 nm over a Concentration Range”
Calculations done on data from graphs should be referenced to the respective graph by its figure or graph number. The graph title should give the reader enough information to explain its contents and purpose without reference to the report. ie “X versus Y’ is not acceptable.
- When plotting the points on a graph use a small “x” or “o” or “.” . Ensure that the plotted points can be clearly identified.
- When drawing the line of best fit, be careful. Only one smooth line or curve should be visible.
- Error bars or error ellipses can be drawn in carefully, if the data is available, but the original point should still be clearly visible.
Temperature ^{o}CG RAPH 1 : Calibration of a Thermocouple
1032SCG Physics 1b
EQUATION OF A STRAIGHT LINE:
y = mx + c
where
m = slope (gradient) of the line
c = y intercept (x = 0)
– _{m}^{c} = x intercept (y = 0)
GRADIENT:
(a) To get the gradient select 2 points from the graph (x_{1},y_{1}), (x_{2},y_{2}) | |||
m = ^{y}2 | – y_{1} | ||
x_{2} | – x_{1} | ||
- If the x and y axes have different units then the slope will have units. Otherwise the slope will be dimensionless.
CONVERTING NON-LINEAR GRAPHS TO STRAIGHT LINE GRAPHS:
- y = cx ^{m}
log y = m log x + log c | cf | y = mx + c |
Plot log y verses log x. | ||
(b)y = ce^{mx} | ||
ln y = m ln x + c | cf | y = mx + c |
Plot ln y verses ln x. |
1032SCG Physics 1b
1.5.5 PLOTTING GRAPHS USING KALEIDAGRAPH
ENTERING DATA VALUES
Formatting and Naming Columns
- Double click on the top of the column. A box should appear.
- In the box on the left hand side, click on the column you wish to name.
- Type the name of the parameter and its units in the white box below this eg Length (m).
- From the Digits pull down menu on the right select the required number of significant figures.
- To change the width of all the columns, enter a value in the Column Width
- Repeat procedure for each column.
- When all columns are finished click
Creating a series:
To save time, you can automatically ‘enter the values for the independent variable into a column by creating a series:
- Click on the top of the column. The whole column should highlight.
- Pull down the FUNCTIONS menu and select CREATE SERIES.
- Enter the Initial Value (this is normally the minimum value).
- Use the Tab key to move down the options or click in each box using the mouse.
- Enter the Increment (the amount you want each value to increase/decrease by) .
. f) Multiplier should be 1 (the amount you want each value to be multiplied by).
- Click on the box to the left of the Final Value to select this option.
- Enter the Final Value (usually the maximum value).
- Click on OK
You will still have to manually enter the corresponding values for the dependent variable( s) in the next column(s) however. To do this simply click in each box or navigate around the boxes using the arrow keys or Tab key and then type in the values. Be careful to include negative signs if applicable.
Entering a Formula
If you wish to compare your experimental results to those predicted using theory, you can enter the appropriate formula and Kaleidagraph will calculate the theoretical values for you.
- Click on the WINDOWS menu and select FORMULA ENTRY (or hit Ctrl and F).
- You should now have somewhere near the bottom of the screen a box which looks like this:
- Click in the box and then type in your formula. You will have to be careful with your syntax, the formula entry is not case sensitive, but you will have to use * to multiply, / to divide and + and – for addition and subtraction. For formulas containing Sin or Cos, make sure the values you wish to perform these functions on are in brackets e.g. sin(c0/3 .14) and that the correct unit (degrees or radians) is selected above the Help
1032SCG Physics 1b
- You will also have to be careful with the order you type the formula in. Like a calculator, Kaleidagraph performs multiplication or division before addition or subtraction so you may need to use brackets. For example to add 1 to your values in column 0, then multiply the answer by 2 and record the result in .column 2, your formula will have to read c2=( c0+1)*2.
- If you have any problems click on the Help
- Click the mouse on the Run The column you entered the formula for should now be filled with values.
Saving and Printing Your Data
- Click anywhere in your data table to make sure it is highlighted.
- Click on the WINDOWS menu and select SAVE DATA AS.
- In the box that appears select a suitable location to save your data to and give your data an appropriate name (it is a good idea to include which part of the experiment it is from to avoid confusion).
- Click Save.
- To print the data, click on the WINDOWS menu and select PRINT DATA then follow the prompts.
CREATING A PLOT
Standard X vs. Y Scatter Plot
Once you have entered and saved your data, click on the GALLERY menu and select LINEAR then
SCATTER. You should see a box that looks like this:
- Select which column you wish to be on the X-axis (the independent variable) by clicking the circle next to the column name under the X.
- Select which column you wish to be on the Y-axis (the dependent variable) by clicking the circle next to the column name under the Y. If you wish to view more than one set of results on the same graph (for example multiple trials of the same experiment) click on the circles next to all columns you wish to include under the Y.
- Click on New Plot.
Double Y-axis Plot
1032SCG Physics 1b
It is sometimes useful to create a plot with a double Y-axis. To do this click on the GALLERY menu and select LINEAR then DOUBLE Y.
- Select which column you wish to be on the X-axis (the independent variable) by clicking the circle next to the column name under the X.
- Select which column you wish to be on the first Y-axis (left hand side of plot) by clicking the circle next to the column name under Yl. Select which column you wish to be on the second Y-axis (right hand side of plot) by clicking the circle next to the column name under Y2.
- Click on New Plot.
Formatting and Labelling Plot
- The default title of the plot will be what you have saved your data as. If you wish to change this, double click on the name of the graph and in the box that appears, replace it with an appropriate one that describes what you are seeing (not X vs. Y). Then click OK.
- The titles of the axes will be the names of the columns so they shouldn’t need to be changed. If you do need to edit these, double click on the axis name and in the box that appears, replace it with the new one. Then click OK. ‘
- To edit the format of the labels or any other features of the plot click on the FORMAT menu and select the required parameters.
- To move the plot or axis titles or the legend, simply click and drag them.
- To change the scale on the X-or Y-axes click on the PLOT menu and select AXIS OPTIONS. In the box that appears, select the axis you wish to change in the box in the top left and enter the required maximum and minimum values in the boxes on the right hand side. Then click OK.
Drawing A Line Of Best Fit
To add a line of best fit through the data points on a scatter plot, click on the CURVE FIT menu and select LINEAR.
- In the box that appears, click on the box next to the data you wish to fit a line to. If you have more than one set of data displayed on the one plot, click on all the boxes you want to fit a line to.
- Click
- To view the equation(s) for the -line(s) of best fit on the plot, click on PLOT and select DISPLAY EQUATION. To move the equation(s) simply click and drag them.
Saving and printing your plot
- Click anywhere in your plot to make sure it is highlighted.
- Click on the WINDOWS menu and select SAVE GRAPH AS.
- In the box that appears, select the same location that you saved your data to and give your plot an appropriate name.
- Click Save.
- To print the plot, click on the WINDOWS menu and select PRINT GRAPIHCS then follow the prompts.
1032SCG Physics 1b
1.6 FAMILIARISATION WITH EQUIPMENT
1.6.2 Cathode Ray Oscilloscope (CRO)
The Cathode Ray Oscilloscope or CRO is one of the most useful laboratory instruments. It is a device which displays graphically changes in voltage with time. Therefore any periodic event can be displayed on the CRO as long as it is converted to a voltage by a suitable transducer.
At the heart of the CRO is the Cathode Ray Tube (CRT). This device is similar to the television screen and allows for the visual display of both an independent (time) and dependant (voltage) axis. The CRT (refer to Figure C) is an evacuated tube containing 3 important parts.
- The electron gun.
- The X and Y deflection plates.
- The fluorescent screen.
Figure C The Cathode Ray Tube
The electrons are focussed to a beam and accelerated to a high speed in the electron gun. The beam then passes through the X and Y deflecting plates and hits the fluorescent screen creating a pulse of light. This is the why the CRO is so useful because it can display visually a graph of the voltage as a function of time.
The electron gun consists of :
- Indirectly heated cathode.
- Control grid.
- Electron lens.
The cathode is a nickel cylinder surrounding the heater coil and is coated with a mixture of barium and strontium oxides which emits electrons at a temperature of about 800°C. The grid is a cylinder with a central aperture, and the adjustment of its potential (negative with respect to the cathode) controls the electron emission and hence the brightness. The two outer disc electrodes are about 1 kV positive with respect to the cathode so as to accelerate the electrons to high speeds, while the potential of the central tubular anode is adjustable so as to provide a focus control.
1032SCG Physics 1b
The X and Y deflecting plates are two sets of metal plates placed at right angles to each other. Each set of deflecting plates consist of two parallel plates with a potential difference between them. This means that an electric field is created between the two plates. From electromagnetism any electron moving in a straight line is deflected off that straight line in the presence of a perpendicular electric field. The amount of deflection is dependant upon the strength of the electric field and therefore is dependant upon the potential difference between the two plates. So that the greater the voltage applied to the plates, the further the electron beam is moved away from the centre of the screen. The X and Y position dials add a “steady” voltage to the plates which deflects the beam to the required position on the screen.
The X deflecting plates are connected to a periodic ramping (continually rising) voltage. (see figure D). For every period of the ramp voltage the electron beam is swept once across the fluorescent screen causing a line to appear. The slope of the ramp determines how fast the electron beam is swept across the screen. The TIME/DIV dial controls the slope of the ramp voltage. The ramp voltage has to be periodic in nature because of the short lifetime of the pulse of light created. If the electron beam was not continually swept across the screen then the image would fade away quickly.
Figure D Ramping voltage used as the time base.
- Electron beam turned on and spot swept once across screen.
- Electron beam turned off. Spot returns to starting position.
The Y deflecting plates are connected to the voltage input signal. However the input signal, which can be in millivolts, has to pass through an amplifier to boost it to the voltages required to deflect the electron beam (up to a few hundred volts). The gain of the amplifier is controlled by the VOLTS/DIV dial.
After passing the X deflecting plates the electron beam is deflected in the horizontal axis and after passing the Y deflecting plates the electron beam is deflected in the Y axis. The net result is a trace of the waveform on the fluorescent screen.
The fluorescent screen is coated with semiconductor crystals such as zinc sulphide or zinc silicate, which emit light when bombarded by electrons. The greater the electron density in the electron beam the brighter the output pulse will be.
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The display of the CRO is similar to a television screen except that it has a grid on it. The voltage versus time graph is plotted on the screen. The X (horizontal) axis is the time axis and the Y (vertical) axis is the voltage axis. The X axis is broken up into 10 divisions (lines) and the Y axis is broken up into 10 divisions (lines) creating a square grid on the screen. The centre lines of the X and Y axis contain tick marks corresponding to 0.2 of a division. The user has control over the scales of the X and Y axis. The scale of the X axis can be changed using the TIME/DIV knob and the Y axis can be changed using the VOLTS/DIV knob.
There are different types of oscilloscopes used in this laboratory. CROs are by no means the same but they do have some common features :
DISPLAY CONTROLS
This controls the brightness of the trace on the CRO. Note that the trace should not be too bright as it can burn the phosphor and destroy the screen.
This controls the sharpness and definition of the trace on the screen.
POSITION CONTROLS
1)
This moves the trace across the screen. The best position for the trace is so that it covers the whole of the grid. However the trace can be adjusted to whatever position is appropriate. This is especially useful when measuring periods of waveforms.
2)
This moves the trace up and down the screen. The best position for the trace is so that it is on the centre line when no signal is coming in. However the trace can be adjusted to whatever position is appropriate. This is especially useful when measuring amplitudes.
SCALE CONTROLS
- Time/Div
This changes the scale of the time (X) axis. Each division of the screen can be made to represent from 0.2 µsecs to 0.5 secs.
- Volts/Div
This changes the scale of the voltage (Y) axis. Each division of the screen can be made to represent from 5 mV to 5 V.
SIGNAL INPUT
- AC-GND-DC
This switch selects the connection between the CRO and the signal: AC (alternating current) interposes a capacitor, so only the alternating component of the signal is passed; or DC (direct current) is a direct connection; GND shorts the input, which is equivalent to zero signal.
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READING THE CRO
(1) Reading A Voltage With The CRO
Refer to Figure A.
Voltage = (number of divisions) ´ (reading on VOLTS/DIV) The VOLTS/DIV dial is set to 2V/DIV The number of divisions peak-to-peak is 4. Therefore
Volts (pp)
= 2 V/DIV ´ = 8 V
4 DIV
NOTE: To obtain an accurate reading expand the voltage scale so that the waveform takes up most of the screen.
(2) Reading Time And Frequency With The CRO
Refer to Figure A. | ||||
Time for 1 cycle | = | (number of divisions) ´ (reading on TIME/DIV) | ||
Frequency | = | 1 | ||
time for 1 cycle |
The TIME/DIV dial is set to 5 msec/DIV
The number of division is 4 divisions
Therefore
time for 1 cycle | = | 5 msec/div ´ 4 div | ||
= 20 msec | ||||
frequency | = | 1 | ||
20 msec |
= 50 Hz.
NOTE: To obtain an accurate reading expand the time scale so that one cycle takes up most of the screen.
Figure. A Voltage, Time and Frequency measurements.
VOLTS/DIV
SWEEP TIME/DIV
2 V/Div
5 msec/Div
(a) | Peak Voltage ……………………. | 2 V/DIV x 2 DIV | = 4 Volts | ||
(b) | Peak to Peak Voltage ………… | 2 V/DIV x 4 DIV | = 8 Volts | ||
(c) | Time for 1 Cycle ………………. | 5 msec/DIV x 4 DIV | = 20 msec | ||
Frequency………………………… | 1 | = 50 Hz | |||
time | |||||
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1032SCG Physics 1b
1.6.3 The Function Generator
The function generator (also known as a signal generator) is an electronic device used to produce a continuous stream of waves in a circuit connected to it. The waveform produced by the function generator is (usually) a voltage which varies with time, i.e., the function generator is usually a voltage source. For example, if the function generator is set to generate a 1 kHz sine wave, it means that the output voltage (the voltage measured at the output terminals) is sinusoidal and repeats every one-thousandth of a second.
The versatility of the function generator is in its ability to change:
- frequency;
- amplitude;
- waveform (the shape of the wave, e.g. sinusoidal, triangular,…).
Not all function generators are the same but they all have common features. Become familiar with the placement of these on the function generator provided.
OPERATING INSTRUCTIONS for G.W. MODEL GFG 8020G
- Turn on at the wall and by depressing the PWR ON/OFF
- Connect the output lead to the OUTPUT 50W
A Default Setting
- Ensure that the DUTY knob is turned to CAL (this makes the output symmetric as to the time spent in the positive and negative half-cycles).
B Setting the Frequency.
- Depress the button corresponding to the frequency range required (1M, 100k, 10k, 1k, 100, 10 or 1 Hz)
- Turn the knob under the display to obtain the desired frequency. NOTE: There is a delay between readings.
- Frequency is read directly from the display in either kHz or Hz
C Setting the Amplitude
- Turning the knob will adjust the peak to peak voltage of the output waveform. NOTE: Ensure the AMPL knob is pushed in.
- When the amplitude of the waveform is adjusted both the positive and negative peaks are adjusted at the same time.
D Selecting the Waveform
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HOW TO WRITE LABORATORY REPORTS
Report Guidelines
LABORATORY REPORT FORMAT
The laboratory reports are to be formal. That is, the laboratory report is recorded in such a way that the experiment could be repeated by a reader of the report. An example of a report is given in the attachment named Sample Report. READ THIS ALL THE WAY THROUGH.
LAYOUT
Formal reports must be generated by a word processor: they are NOT to be hand written. (MS-OfficeTM is available for use on computers in the Learning Centres). Similarly it is best to use drawing and graphics programs (e.g. the drawing package in MS-Office Word, or MS-Paint, or AutoCAD) for producing images and diagrams.
The report must be laser, or ink-jet, printed on ONE SIDE of A4 sized paper. Colour printing is acceptable but not required. Do NOT make it ‘fancy coloured’. Overly ‘artistic’ reports are NOT professional.
Reports are to be stapled in the upper left-hand corner only. Do NOT submit reports in binders, plastic folders, or other ‘fancy coverings’. (This just makes it difficult to read, mark and store).
WORDING
The reports are written in the third person. This means that NO gender or person-referencing titles are to be used. That is, do NOT use words like: I, me, we, he, students, etc. For example; instead of writing: ‘I measured the result to be’, write ‘The result was’. Also, instead of: ‘I moved the actuator and the group noticed a glow’, write ‘The actuator was moved, and a glow was detected’.
The report must be in proper English, with correct sentence structure. Also the report will be written in correct tense (i.e. do not incorrectly use, or mix, past, present, and future tenses). For example, the following has incorrect tense: “The load will be added, and the beam was bent”. Slang and inappropriate abbreviations are NOT to be used.
COVER SHEET
A cover sheet is required and must be printed off the Learning@griffith website and filled in using a pen. Fill in every box. This is the only part of your report that you do not word-process. Attach the cover sheet as the front page of your report.
REPORT SECTIONS: The report should contain the following sections.
AIMS:
The original aim or purpose for undertaking the experiment should always be recorded. Usually the experiment aim / aims will be given in the laboratory notes provided for the particular experiment.
Note: Do NOT alter or re-word any given aim.
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INTRODUCTION:
Depending on the intended audience of the report, the introduction may or may not be needed. When you are writing the report for peers of similar educational background, the introduction may not be necessary. However when the intended readers have little knowledge of the report’s subject matter, an introduction is vital.
For formal lab reports you ARE expected to provide a brief introduction.
The introduction should explain to the reader (in layman’s terms) the relevance of the subject matter (the relevance to the experiment), why it was necessary to undertake the report (or experiment), and what benefit the results will be to them or others. In the process, some background information (or theory) to the subject matter may be required.
APPARATUS:
Usually ALL equipment used during the experiment must be listed. This list should include the FULL complete name of the given equipment, along with the equipment identification numbers,
For example: The following will be INCORRECT
Multimeter,
Vernier Calliper.
The following is CORRECT
Fluke DM234 Multimeter, ID 1334566, Matsumoto MD54 Vernier Calliper, ID 846626.
PROCEDURE:
The procedure must be recorded within the report. This is not only to aid in replication of the experiment, but it also conveys to the more concerned reader exactly what the following results and calculations relate to, within the report.
The procedure will be basically as in the Laboratory Notes that have been provided for the particular experiment. However you must change the form when you write this down. The Laboratory Notes consist of a set of instructions (orders) to students. In a formal report, an researcher does not give orders to the employer who commissioned the report! Therefore the Procedure section will be written in the past passive. (To see what is meant by this, look at the Procedure in the Sample Report given below).
RESULTS:
All data, tables, graphs, and diagrams should be recorded in their entirety within the results section. (That is, replicate ALL results that you recorded in your laboratory notebook or in the tables supplied in the Lab Notes.). The results should be neatly presented and completely understandable.
The results section generally contains as little wording as possible, and all explanations of the results should be within the procedure or discussion section. However the results should be intelligible on their own, without the need for reading any other section of the report. Thus, ALL results need an initial explaining sentence.
Diagrams, like pictures, can convey more information than paragraphs of words. Thus never try to explain something in words that could be better explained by a diagram. Each diagram must contain a descriptive title, that provides enough detail that makes the diagram understandable, independent of the rest of the report. (Titles such as: “Task 3 Part C” is not descriptive enough). Where possible, multiple result readings should be tabulated. ALL results must have units on the measurement (such as: m [meters], kg [kilograms]), and the results should only be given to the accuracy valid from the initial observations.
Length = 15.3299547482 (is always WRONG). Length = 15.33m (is correct).
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1032SCG Physics 1b
ALL graphs and calculations must be formatted correctly, (See the paragraphs below).
Format of Graphs:
Graphs must have a name at the top of the graph, and the name must be meaningful. For example; ‘Graph of Time Vs Distance’ would NOT be acceptable. The name should be more explanatory, such as: ‘Graph of the Time of Fall for objects falling a 2m Distance, for Experiment 1B’. This detail is necessary so that the graph is understandable, independent of the rest of the report.
Do NOT label graphs as: Graph of X vs Y, or ANY other derivative of the Horizontal and Vertical axis labels. For example, assume an experiment requires the measurement of the Voltage and Current recorded from a heating light bulb. In this case do NOT label the graph as: Graph of Voltage and Current. That label is NOT descriptive, and says nothing more than what could be determined by looking at the Horizontal and Vertical axis. Instead label the graph as something like: ‘Graph of the Response from a Heating Light Bulb’.
The Horizontal and Vertical axis must be scaled. That is, have ruled axis with numbered tick marks. Each axis must be named (such as ‘Fall Distance’), have the symbol (such as ‘d’), and have units (i.e. cm). Note that Microsoft Excel (part of the Microsoft Office package available on University computers) can make adequate graphs.
If you need to determine which recordings go on which axis; then the general rule is:
The Independent Variable (the one that is set, given, or altered by the user during the
experiment) is plotted on the Horizontal Axis, while the Dependent Variable (the one that
depends on the independent variable, the unknown, measured or calculated value) is
plotted on the Vertical Axis.
Format of Calculations:
For ALL experiments, all calculated results must have a valid estimation of the error in the result. The error estimate can be calculated by the methods described in the front of your Lab notes.
DISCUSSION:
The discussion should give an overview of the final results obtained. Each result obtained should be discussed, even if the result was as expected. Avoid discussions that are worded as “first this was done, and then that was done, ……, and finally this was done”.
Also, avoid rehashing anything that is already stated in previous sections of the report, (such as the introduction).
A full discussion on any discrepancies between expected and observed results will be required, as well as a discussion on any unusual results. Also discuss any tasks that were not completely solved.
Avoid simple statements such as –“it didn’t work”. Instead discus why did it not work, and how could this be solved.
Any questions asked or implied within the Laboratory Notes will be answered in this section.
However, do NOT just answer the questions as in an exam (the employer has not seen the Lab Notes!) Instead a full paragraph on each question is required, that will include the original question and the answer to the question, with clear and logical sentence structure. For example, assume the Lab Notes contained the question: ‘Do the two objects fall in the same time?’. In this case NEVER just answer this as something like:
‘Yes they both have the same time’, or worse, just ‘Yes’. Instead effectively state the question and the answer in complete sentences, something like: ‘It was observed that the first object took 0.25 ± 0.02 s during the fall, and the second object fell in 0.26±0.01 s. Thus it is concluded the two objects fell at the same speed, to within
experimental accuracy.’
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What we are looking for here is some understanding of what went on in the experiment. A discussion of the PHYSICS is important.
CONCLUSION:The conclusion is generally the most important section of the report. Usually the conclusion is the only part of the report that is read by the executives in the organisation that commissioned the report. A conclusion should be drawn from the results, and the aim of the experiment should be answered. For example; if the aim was to determine the value for the acceleration g due to gravity, then the value and the associated error should be reported. Any conditions on the value, (such as major errors or inconsistencies), should be stated. Finally, if possible, the result should then be compared to the known standard.
The conclusion could also include, in a brief, any unique skills learned or major problems solved during the experiment.
REFERENCES:
All foreign material and literature sources used within the report should be recorded. Each reference will be required to be in the Harvard Style of Referencing. (Which request the reference to have: the author, the reference title, book name, publisher, date of publication, and page numbers used.
See the following web sites for more details on the referencing styles:
http://www.griffith.edu.au/ins/training/content_howtoguides.html http://www.griffith.edu.au/ins/copyright/content_citation.html
(It is acceptable to reference the Lecture Notes or Lab Notes if appropriate. You do not necessarily have to find outside sources, but if you do use them you should reference them)