Physics Laser Project

See Akram's blog http://physics4cahkhan.blogspot.com/

Experiment 15: Planck's Constant From and LED

Introduction: The purpose of this activity is to experimentally determine the value of Planck's Constant using a diffraction grating and a variety of LED's

Activity One: The energy given to an electron under a a potential difference is E=qV where q is the charge of an electron and V is the voltage potential difference. The energy of an electron also is (h•c)/lambda where h is Planck's constant, c is the speed of light, and lambda is the wavelength of the light source. Setting them equal to each other, we get q•V=(h•c)÷lambda. Solving for h, we get h=(q•v•lambda)÷c.

Activity Two: Procedure: We attached a resistor to the positive of a voltage source set at 3 volts and one end of and LED. We then attached the Other end of the LED to the negative of a voltage source. We then set up a two meter stick with a diffraction grating at the end opposed to the LED and a one meter stick perpendicular to the first.

We looked through the diffraction grating and marked on the one meter stick where the spectrum began and ended. We did this for all the colored LED's and noted the voltage.

Data and Analysis: Here is the data collected on all of the different colors of LED's. We used the same formula from light and spectra (lambda = (d•D)÷√(L^2–D^2)) to find the wavelength of all the LED's. The value of d is given as a difference because the spectrum is not just a line, rather a smear. All of our group members looked through the grating to give 3 trials for every color

The colored LED's only displayed their color when looking through the diffraction grating for the most part. As observed in the picture, blue displays mostly blue a slight bit of green and green displays mainly green a small amount of blue. Yellow, however, displays a little red, orange and green on top of the yellow. The most likely explanation for this is the LED's are not pure forms of their color. In the case of yellow, the shade of yellow is emitting a larger portion of the visible spectrum than just yellow but the majority of the light emitted is yellow. Of course, white emits the entire spectrum. The LED with the largest error is yellow. This is due to the width of the spectrum displayed as just discussed. Below are the data and calculations for lambda and Planck's constant as well as the uncertainty associated. It was planned that we would graph Voltage versus 1/lambda, however this gave a split graph and threw of the linear fit of the slope, which would give Planck's constant. To correct this, we found the value of Planck's constant using the formula from activity one for every color and averaged them. This gave us a more accurate value for Planck's constant.

Questions: We did not see a relationship between wavelength other than green and blue used more voltage than yellow and red. This makes sense because those are more high energy wavelengths. This can be applied to sunset being red and the sky being blue. The sunset will be red because red is a less energetic wavelength and will be refracted by the atmosphere last.

Experiment 14: Color and Spectra

Introduction: The purpose of this experiment is to measure the wavelengths of the various colors in the light spectra as well as observe the colors emitted by single elements using a diffraction grating.

White Light Procedure: We placed a light source on a table and attached a diffraction grating to a 2 meter stick touching the light source. We then put another meter stick perpendicular the first touching the light source

We then looked through the diffraction grating and observed the entire light spectrum and marked where the various colors began and ended.

Data and Analysis: The diagram and formula below was used to find the wavelengths expressed in visible light

The work for finding the wavelength and the uncertainty associated is below. The actual value is also compared. Our data is supported fairly well.

Single Element Procedure: 

The set up is the same as with the white light source except the light source was replaced with a hydrogen gas tube.

The tube was looked at through the diffraction grating and only three lines were visible. There are actually 4 but only 3 can be seen.

Data and Analysis: We used marked the meter stick where the lines were and used the same formula to calculate the wavelength with uncertainty for the three lines.

The actual wavelengths visible for hydrogen are 410, 434, 468, and 656 nm. only the 434 nm is within uncertainty. This is probably due to the fact that the meter sticks were not exactly touching the hydrogen tube and the diffraction grating was a cheap plastic one.

Experiment 13: Polarization of Light

Introduction: The purpose of this experiment is to witness the polarizing of light and its effect. This is achieved by observing light through a number of polarizing filters and collecting data.

Preliminary Questions:

1) When the polarizing filters are perpendicular to each other, no light is able to pass through. It looks black

2) This is a graph of light intensity versus Rotation angle from 0 to 180 degrees

Procedure:

We attached two polarizing filters to a meter stick in front of a light source and secured alight sensor to it. The polarizing filters were positioned so the most amount of light would come through and were marked. They were then rotated so the least amount of light would come through and were marked. The brightest angle is referred to as 0º and the darkest as 90º

We then collected data on light intensity versus angle of rotation and rotated the second polarizer 7.5º at a time clockwise until we turned 90º. We then did the same thing counterclockwise.

We then moved the second polarizer out of the way and we adjusted a third polarizer to block out as much light as possible and then replaced the second polarizer at the 0º position. We rotated the second one 7.5º at a time just as in the previous step and generated another graph

We then looked at florescent light through a polarizer and then the reflection from a florescent light on the table

Data and Analysis: 
For the two polarizers

The first graph explains that the polarizer filters out light as a function of angle as a sin pattern. This means as you turn it from parallel, the light becomes less and less intense until tapering off to zero, and then it gradually becomes brighter, then quickly becomes brighter, and then brightness slows its speed until you have turned it 180º. The cos^2 graph vs illumination is linear.

For three polarizers

Our graph does not reflect what should happen. Since the first and last lens are perpendicular to each other, the light should not come out, however the middle lens shifting some of the light emitted from the first lens so all of the light is not blocked by the third lens. This means that 45º should yield the most light because it creates the least similar alignment with either the first or third lens. Towards the end of our graph, this becomes clear.

When looking directly at the florescent lights through the polarizing filter, there is no observable change when the filter is rotated. This is because florescent lights are random emitters of light, meaning that they release light at all orientations. If the rotation cancels one, a new one will replace it. This is not so with the reflection of light. The table is not a perfectly reflective surface so the contours of the table partially orient the light. The polarizing lens is able to block light of the specific orientation so when rotated, the reflection of the light will darken.

Experiment 12: CD Diffraction

Introduction: The purpose of this procedure is to measure the distance between the burned in grooves of a CD using a laser by analyzing its diffraction pattern.

Procedure: We first found the wavelength (lambda) for the laser. We did this by shining a laser through a diffraction grating at a wall. We measured the distance from the grating to the wall (L) and found the distance between the slits on the grating (d) by dividing .001 meters by 600, because that was the number of lines per millimeter. We also determined theta by measuring the distance between the primary laser spot and the brightest maxima (y) and using some trig identities.

We then cut a hole in a piece of paper and held it upright over the table parallel to a CD.

We measured the distance between the CD and the paper and directed the laser through the hole onto the CD. We then measured the distance between the middle and one of the outer laser dots.

Data and Analysis: 

This is the calculation for theta from the first picture with uncertainty.

This is the calculation for the wavelength of the laser with uncertainty. The value printed on the laser was 650 nm so our result is confirmed.

This is the calculation for the distance between the groves in  the CD (d).

This is the percentage error of the industry standard of the distance between the groves (1600 nm) and the experimental value.

We found uncertainty for all values by finding the maximum and minimum values of the required variable which were as a result of uncertainty in measurement. We then average the max and min and subtracted the average from the max, and the min from the average. For d, the value was found to be 1573.5 nm ± 189.5 nm. The industry standard is within this uncertainty value so our results are confirmed.

Experiment 11: Measuring a Human Hair

Introduction: The purpose of this experiment is to use diffraction to accurately measure a human hair. The measurement will be confirmed with a micrometer.
Procedure: We hole punched a card and taped a hair taught over the hole. We then shined a laser through the hole, over the hair.

We then measured the distance from the card to the wall we would project the laser beam on with a 2 meter stick. This value is referred to as L.

We measured the spaces between the bright spots of the interference pattern, noting the uncertainty of the measurement. This value is referred to as y. The wavelength (represented as lambda) was stated on the laser.

Data and Analysis:

We used the formula in the picture and solved for d. In this formula, d is the measure of the gap between the light beam that causes the interference pattern. In this case, it is the diameter of the hair. We then calculated the maximum and minimum values of d, which came from the uncertainty in the measurement of y. We averaged them together and then subtracted the average from the maximum of d, and the minimum of d from the average. This gave the uncertainty of d. This yields the value of d  to be 5.4e -5 ± 0.25e -5. This measurement makes sense because the hair must be on the order of magnitude of the laser wavelength or smaller to cause interference. This answer is smaller than 650 nm. The d experimental is the measurement of hair obtained by the micrometer. It is not within uncertainty however, this is likely because the micrometer was not calibrated before measurement and was in a very used condition. It is on the same order of magnitude so we were in the right ballpark with a percentage error of 25.9%

Potential Wells

1. The ground state was 2.1 MeV regardless of a finite or infinite potential well.

2. The first excited state was 8.4 MeV for the infinite potential well. It is not possible for the 8.4 MeV to exist in the finite potential well.

3. The energy of the first excited state is higher in the infinite well than the finite because the wavelength is larger for the finite potential well which translates to lower energy.

4. When the potential well is lowered, the particle's energy is closer to the top of the potential well which means it can penetrate deeper

5. It will penetrate less

Potential Energy Diagrams

1. The range of motion will be between -5 cm and 5 cm.
2. The particle can not cross the barrier because its total energy is less than that of the potential barrier.
3. There is more of a chance of detecting the particle between -5 cm and 0 cm because the potential is higher there than between 0 cm and 5 cm. This means that you must subtract the potential from total to get kinetic in the region -5 cm to 0 cm which is smaller than the kinetic in the region 0 cm to 5 cm where the potential is 0.
4. The motion will increase by a factor of root 2.
5. It will be an upside-down parabola.
6. Near the endpoints of the graph because the particle is moving slower at the ends.

Relativity of Length Activity

Question 1: Yes. The movement changes the observed distance.
Question 2: Longer due to time dilation.
Question 3: Yes. It must in order to withhold the Lorentz factor relationship.
Question 4: It would be 769.23 meters while moving.

Relativity of Time Activity

Question 1: The distance is greater for the moving frame than for the stationary one.
Question 2: The moving frame will experience a longer time interval.
Question 3: No, the rider would experience the same result as the stationary frame because it is the equivalent of a stationary frame of reference.
Question 4: There would be less of a difference in time experienced if the velocity was decreased because the distance the light traveled in the moving frame of reference would decrease.
Question 5: It would be the time measured by the observer riding the light clock multiplied by the Lorentz factor. in this case it is 8x10^-6 seconds for a time of 6.67x10^-6 and a Lorentz factor of 1.2.
Question 6: The Lorentz factor would have to be 1.1169

Experiment 7: Reflection and Refraction

Introduction: The purpose of this experiment is to examine some simple examples of reflection and refraction and relate them to Snell's law

Procedure: We set up a light box with a slit of light pouring out. We then directed that slit at the flat side of an acrylic semicircle. We set the semicircle on a protractor and rotate the entire set up to measure the angle of refracted light coming out the other side. We did this for 10 trials, taking data down starting at 10 degrees and ending on 70 degrees.

 We then attempted to do the same thing on the rounded side of the acrylic semicircle but were forced to stop at 44 degrees, only taking down 8 data sets.

Data:

Flat side of acrylic:

Theta 1 (degrees)	Theta 2 (degrees)
10	7
15	12
20	14
30	20
35	23
40	25
45	30
50	32
60	36
70	41

This is Theta 1 vs. Theta 2

Sin(Theta 1) vs. Sin(Theta 2)

Round side of acrylic:

Theta 1 (degrees)	Theta 2 (degrees)
0	0
5	7
10	15
15	24
20	35
30	53
40	75
44	90

Theta 1 vs. Theta 2

Sin(Theta 1) vs. Sin(Theta 2)

Analysis: We were not able to complete the 10 trials on the round side of the acrylic because we witnessed total internal reflection at 44 degrees. This is the last angel we could muster before total internal reflection.

The equation of the line from the flat side of the acrylic can be rewritten as sin(theta 1)/sin(theta 2)=1.48. Rearranging Snell's law, sin(theta 1)/sin(theta 2)=n two/n one. Therefore, 1.48 equals n of air/n of acrylic, given n one is air in this case. For the rounded side of the acrylic, the equation of the line can be rewritten as sin(theta 1)/sin(theta 2)=0.667. Using the rearranged version of Snell's law, 0.667 equals n of air/n of acrylic, given that n one is acrylic in this case because the light is being refracted after it has already entered the acrylic. Indeed, the second slope is the inverse of the first one.

Experiment 5: Introduction to Sound

Introduction: The purpose of this lab is to record different sound waves and analyze the differences in their wavelengths, amplitudes, and frequencies.

Procedure: Have a person say aaaaaa into a microphone and collect the sound wave data.

We then had a different person say aaaaaaaaa into the microphone and recorded the data

We then struck a tuning fork hard and then soft and recorded both results in a microphone

Data:

First person's voice

Second person's voice

Tuning fork struck hard

Tuning fork struck soft

Analysis: 

1-a) The wave is periodic because of its definite repeating pattern

1-b) We determined four waves by only counting the completed ones

1-c) The sound was only captured for .03 seconds so about a blink of an eye

1-d) The period is 7.5 x 10^-3 seconds. This was decided upon by counting the number of waves and dividing the total time of the sample by that number

1-e) Frequency is 1/period = 133 Hz

1-f) velocity=wavelength x frequency so wavelength=velocity/frequency which is 2.55 meters; about the length of a lab desk

1-g) The amplitude can not be determined because there is nothing to reference it against, but there was an arbitrary pressure of about 2.7.

1-h) The only thing that would change is the amount of waves on the graph. Everything else would stay relatively unchanged.

2) Period=1.67 x 10^-3, frequency=600 Hz, nearly 4 times greater than the first, wavelength=0.567 m, nearly 4 times shorter than the first, amplitude is roughly the same.

3) Period=3.75 x 10^-3, frequency=2.67 Hz, wavelength=1.275 m. The wave is much smoother and uniform than a human voice.

4) Nothing changed but the amplitude and the smooth nature of the wave. We hit the fork on a softer object to make it softer.

Experiment 4: Standing Waves

Introduction: The purpose of this experiment is to observe the relationship between wavelength, frequency, and wave velocity at resonant conditions on a standing wave on string.

Procedure: We attached an oscillator to a frequency generator.

We then attached a length of string to a frequency generator via a clamp.

We put the other end of the string over a pulley and attache a 200g mass to it.

We changed the frequency of the frequency generator until we got 2 nodes and measured the distance between the nodes.

We did this for 3 nodes and 4 nodes up until 12 nodes and recorded the lengths between each.

We then replaced the 200g mass for 1/4 of it or 50g and repeated the entire process, only recording 7 different node distances rather than 11.

Data:

Case 1: 200g mass

Number of nodes	Frequency (Hz)	Distance d between nodes (m)	λ=2d (m)	1/λ	n=2L/λ (L=1.97)
2	22	1.97	3.94	0.253807106598985	1
3	44	0.98	1.96	0.510204081632653	2.01
4	59	0.652	1.304	0.766871165644172	3.02
5	77	0.44	0.88	1.13636363636364	4.48
6	97	0.393	0.786	1.27226463104326	5.01
7	120	0.33	0.66	1.51515151515152	5.97
8	130	0.295	0.59	1.69491525423729	6.68
9	170	0.245	0.49	2.04081632653061	8.04
10	190	0.215	0.43	2.32558139534884	9.16
11	200	0.185	0.37	2.7027027027027	10.6
12	215	0.175	0.35	2.85714285714286	11.3

  

 Case 2: 50g mass

Number of nodes	Frequency (Hz)	Distance d between nodes (m)	λ=2d (m)	1/λ	n=2L/λ (L=1.887)
2	10	1.887	3.774	0.264970853206147	1
4	29	0.662	1.324	0.755287009063444	2.85
5	34	0.481	0.962	1.03950103950104	3.92
6	50	0.395	0.79	1.26582278481013	4.78
7	59	0.33	0.66	1.51515151515152	5.72
8	70	0.277	0.554	1.80505415162455	6.81
14	130	0.115	0.23	4.34782608695652	16.4

Mass of String: 0.99g +/– 0.01g

Experimental mass of 200g mass: 199.9g +/– 0.01g

Experimental mass of 50g mass: 49.89g +/– 0.01g

String Length (oscillator to mass): 2.66m +/– 0.1m

Mass per unit length: 3.72 x 10^-4 kg/m

Analysis: Here is a graph of the inverse of wavelength versus frequency. The slope should represent the wave velocity.

Using the equation velocity=sqrt(Tension/mass per unit length), we get velocity=72.62 meters per second. That yields a percentage error of 4.91%. There exist uncertainty in both the equation value and the graph value, however I assumed the equation value to be the true value here. There is a small uncertainty that comes from the the measurement of the length and mass of the string as well as the fact that the string and pulley are not ideal. This is very small and that is why the equation can be assumed more accurate than the graph data. The graph data relies on the distance between nodes which was more difficult to measure. For one, we could not bring the meter stick too close to the string while it was vibrating. Also as the nodes became more numerous, it became difficult to pinpoint the point of stillness on the vibrating string. These measurements were less accurate and will most likely account for this error. The final contribution is the uncertainty of the frequency generator, given the lack of precise markings on the knob.

Here is the same graph for case 2

The ratio case 1/case 2 for velocity from the graphs is 2.64. The ratio of velocity from the equation is 2.00. The ratios are not equal, but similar. The difference here is probably due to the inability to measure the distance between nodes accurately as well as the uncertainty of the knob on the frequency generator. The values are close so it can be assumed that the measurements were close to the true measurements.

The resonant frequency times n does not equal the set frequency for any value in case 1, but they are relatively close. This can be caused by any of three things: the wave velocity used is inaccurate, the value for n is incorrect, or the frequency recorded from the knob is wrong. It is probably a mixture of all but given how the velocity is derived, it is one of  most influential factors.  The other is the value for n. It is certainly incorrect because n is always one number less than the number of nodes.

The frequency for case 1 is just about double that of case 2 for the same harmonic. This makes sense because we used 4 times the tension in case 1 compared to case 2, and the formula for velocity includes tension under a radical.