Color and Spectra

The purpose of this experiment was to view the spectrum of colors found in white light through a filter to find the wavelength of different colors.

Equipment:
-Uncoated fluorescent lamp
-2 meter sticks
-Diffraction grating
-Hydrogen tubes

Part One:
In this part of the experiment we set up a 2 meter and a 1 meter stick orthogonal to each other in a "L" formation. The light source was place at the joint of the "L" and the diffraction grating was placed at the end of the 2 meter stick. The diffraction grating we used was 500 grooves per millimeter. One partner viewed through the diffraction grating to the light and another moved a pencil along the 1 meter stick until it reached the edge of the spectrum and recorded the distance from the light source. The same was done to find the end of the spectrum.

Data Analysis:

We recorded multiple measurements to find the standard deviation and a more accurate uncertainty.

We also found an experimental linear equation:

Part Two:
We did the same experiment as above, but we replaced the light source with a hydrogen gas tube. With the hydrogen gas tube we saw distinct lines.

Data Analysis:

 All of our values agreed within the accepted values of the wavelengths of violet, teal, yellow, and red light.

Experiement: Potential Energy Diagrams

Potential Energy Diagrams:
A particle of energy 12 x 10^-7 J moves in a region of space in which the potential energy is 10 x 10^-7 J between the points -5 cm and 0 cm, zero between the points 0 cm and +5 cm, and 20 x 10^-7 J everywhere else.

1. What will be the range of motion of the particle when subject to this potential energy function?
- The range of motion will be between -5 and 5 cm.

2. Clearly state why the particle can not travel more than 5 cm from the origin.
- The particle can not travel more than 5cm from the origin because the particle does not have enough energy to go over the potential energy barrier.

3. Assume we measure the position of the particle at several random times. Is there a higher probability of detecting the particle between -5 cm and 0 cm or between 0 cm and +5 cm?
- There is a higher probability of detecting the particle between -5 and 0 cm because there it will ahve less kinetic energy, making the particle slower.

4. What will happen to the range of motion of the particle if its energy is doubled?
-The range of motion will increase if the energy is doubled.

5. Clearly describe the shape of the graph of the particle's kinetic energy vs. position
- The shape will be a concave down parabola.

6. Assume we measure the position of the particle at several random times. Where will the particle most likely be detected?
-The particle will most likely be found at the edges.


Potential Wells:

A particle is trapped in a one-dimensional region of space by a potential energy function which is zero between positions zero and L, and equal to U₀ at all other positions. This is referred to as a potential well of depth U₀.
Examine a proton in a potential well of depth 50 MeV and width 10 x 10^-15 m.

1. If the potential well was infinitely deep, determine the ground state energy. Is this also the ground state energy in the finite well?
- E1(infinite) = (n^2*h^2)/(8*m*L^2)
        = 1*(6.63*10^-34)^2 / (8* 1.67*10^-27 *(10*10^-15)^2)1
        = 3.29*10^-32 J = 2.05 MeV
 E1 (finite) = 1.80 MeV

2. If the potential well was infinitely deep, determine the energy of the first excited state (n = 2). Is this also the energy of the first excited state in the finite well?
-E4(infinite) = E1 * 2^2= 8.20 MeV
 E4 (finite) = 6.80 MeV

3. Since the wave function can penetrate into the "forbidden" regions, will the energy of the first excited state in the finite well to be greater than or less than the energy of the first excited state in the infinite well? Why?
-The energy in the finite well will be less than that of the infinite well because there is a greater probability of tunneling.

4. Will the energy of the n = 3 state increase or decrease if the depth of the potential well is decreased from 50 MeV to 25 MeV? Why?
- The energy of the second exited state will decrease if the depth is decreased because there will be less tunneling.

5. What will happen to the penetration depth as the mass of the particle is increased?
- If the mass of the particle is increased, the depth of the penetration will decrease.

Experiment: Time and Length Relativity

Relativity of Time:



 

1. How does the distance traveled by the light pulse on the moving light clock compare to the distance traveled by the light pulse on the stationary light clock?

-The light travels a longer distance by the factor of gamma in the moving frame than the stationary frame.

 2. 
Given that the speed of the light pulse is independent of the speed of the light clock, how does the time interval for the light pulse to travel to the top mirror and back on the moving light clock compare to on the stationary light clock?

-The clock in the moving frame is 2.73 micro second longer than that of the stationary frame.

3. Imagine yourself riding on the light clock. In your frame of reference, does the light pulse travel a larger distance when the clock is moving, and hence require a larger time interval to complete a single round trip?

-No, there wont be a larger distance, nor longer time interval.

4. 
Will the difference in light pulse travel time between the earth's timers and the light clock's timers increase, decrease, or stay the same as the velocity of the light clock is decreased?

- As the velocity id slowed down, the difference in the timers will decrease because they will be less relativistic and more classical.

 

 5. 
Using the time dilation formula, predict how long it will take for the light pulse to travel back and forth between mirrors, as measured by an earth-bound observer, when the light clock has a Lorentz factor (γ) of 1.2.

-  Δt = γ*Δt(proper)

   Δt = (1.2)(6.67 µs) = 8.00 µs

 

6. If the time interval between departure and return of the light pulse is measured to be 7.45 microseconds by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?

-  Δt = γ*Δt(proper)

   7.45µs = (γ)(6.67 µs) 

   γ = 1.12 

 

Relativity of Length

 

 

1. Imagine riding on the left end of the light clock. A pulse of light departs the left end, travels to the right end, reflects, and returns to the left end of the light clock. Does your measurement of this round-trip time interval depend on whether the light clock is moving or stationary relative to the earth?

- The clock that is moving relative to earth will measure a longer time for the round trip distance than then the one stationary relative to earth.

2. Will the round-trip time interval for the light pulse as measured on the earth be longer, shorter, or the same as the time interval measured on the light clock?

- The time interval for the light pulse will be longer by a factor of gamma.

 

3. You have probably noticed that the length of the moving light clock is smaller than the length of the stationary light clock. Could the round-trip time interval as measured on the earth be equal to the product of the Lorentz factor and the proper time interval if the moving light clock were the same size as the stationary light clock?

- It could be the equal if the Lorentz factor is equal to one, which means that they would be traveling at non-relativistic speeds.

 

4. A light clock is 1000 m long when measured at rest. How long would earth-bound observer's measure the clock to be if it had a Lorentz factor of 1.3 relative to the earth?  

- L = Lp / γ

  L = (1000m) / 1.3 = 769.2 m

 

 

Experiment: Polarization of Light

The purpose of this lab was to observe the change in the light intensity passing through polarizing filters and to measure the transmission of light through two polarizing filters as a function between their axes.

Equipment:
-Logger Pro
-Light Sensor
-Light beam source
-Polarizing filters
-Protractor

Preliminary Questions:
1. When I placed one polarizing filter on top of the second at right angles to each other, no light passed through the orthogonal filters.

2. When we rotated the filters to that their axis were 180 degrees, most of the light passed through the filters. As we changed the angle of rotation towards 90 degrees, less and less light was transmitted through the filters.

Part One:
We mounted two polarizers lined up bother with the 0 and 180 degree on the polarizer holders on a ruler. We then set up the two polarizers parallel to each other so that the beam source, polarizers, and the viewing points are lined up horizontally. We then turned the second polarizer to the 90 degree mark, while leaving the first polarizer at the 0 degree mark. We then connected the light sensor up to the computer and placed it behind the second polarizer. We then used the file Experiment-31 from the experiment files. We then defined the light level as zero by zero-ing the instrumentation. We then returned the second polarizer to the zero position aligned with the first polarizer. To start the experiment, we then rotated the second polarizer 15 degree clockwise. We then recorded the intensity of the light. We kept turning the polarizer 15 degrees until we rotated it 180 degrees.

Data Analysis:

 

 

 

The shape of these graphs are supposed to be sinusoidal. The show that when the polarizers were orthogonal to each other, the light intensity was at a minimum and when they were parallel to each other, the light intensity was at a maximum.

Part Two:

We then temporarily moved the second polarizer out of the way and put a third polarizer behind the first polarizer so that the light passing through the first and third polarizer is as dim as possible. We then put the second polarizer back in the next to the third polarizer on the opposite side of the first. We adjusted the second polarizer to the 0 degree position. It should appear dark. We then rotated the second polarizer and recorded the intensity every 15 degrees clockwise and counter clockwise. 

Data Analysis:

Polarization Upon Reflection:

1. The light from the flourescent bulb does not have any polarization to it.

2. The reflected light does have polarization to it because a spot on the table goes dark because the light was polarized perpendicular to the table.

Conclusion:

The graphs from the experiment were not perfectly sinusoidal because the room was not perfectly dark and the light from other labs could have interacted with the light intensity that was recorded by the light sensor, but they still show the relationship between the angle of polarization and the light intensity.

 

 

Experiment: CD Diffraction

The purpose of this experiment to analyze the diffraction pattern that results from a CD being stuck with a laser.

Equipment:
-Laser
-CD
-Large screen with small central hole
-Meter stick
-Stands and clamps

In this experiment, we arranged the laser, screen, and CD so that the laser shinned through the hole in the screen and struck the CD perpendicularly on the recordable side.

 

When the beam struck the disk perpendicularly at the grooves, the first order maxima appeared on the screen on both sides of the hole. We then measured our x and L distanced and analyzed the diffraction pattern to calculate the distance between the grooves on the CD. 

 Our measure value for the distance between the grooves on the CD was 1535 nm. The accepted value given by the manufacturer is 1600 nm.

The percent error is = (1600-1535)/(1600)*100% = 4.06%

This percent error could have come from the fact that the observed maximas we big blurred dots which meant that we estimated the distance between the first maxima and the center of the laser ray.

Experiment: Width of a Human Hair

The purpose of this experiment was tho measure the thickness of a a human hair.

Equipment:
-Laser pointer
-3x5 card with hole punched
-Human Hair
-Whiteboard

In this experiment we taped a human hair across the hole of a 3x5 card and clamped the card parallel to the wall several meter away from the whiteboard. We then mounted the laser so that it pointed perpendicularly toward the whiteboard through the hole in the card. We then turned on the laser and adjusted the card so that the beam went right through the hair. This then produced a diffraction pattern on the whiteboard. We then measured the distance between the minimas.

(The picture above shows the beam going through the hole in the card)

(This picture was the diffraction pattern on the white board that we analyzed)

Below is our data and data analysis:

Experiment: Lenses

The purpose of this lab was to explore the type of images that are formed at different abject distances and develop a relationship between the object distance and the image distance.

Equipment:
-Optics Bench
-Light
-Object
-Lens and lens holder
-Whiteboard

First we determined the focal length of the lens by using a distant object such as the sun to find a convergance at a focal point. We determined the focal point pf our lens to be 8 cm.

We then set up our apparatus (below) and we varied the position of the object, lens, and the image screen and tabulated the image height, magnification and the type of image that we viewed.

Below is the data:

When we changed the object distance to .5f (4cm) there was no image. This was because at this point it was a virtual image. If you looked through the lens at the object and viewed the image, you could see the image but it was magnified.

We then plotted a graph of the image distance vs the object distance using centimeters.

We then created a new column of data for the inverse image distance and the negative inverse object distance and plotted a graph of the inverse image distance vs the negative inverse distance.

This graph's slope is y=1.027x+.1099. The y-intercept of this graph is the inverse focal length of the lens that we used. Therefore, the theoretical focal length is 9.11 cm.

The percent error for our focal length is: % Error = (9.11-8)/9.11 * 100% = 12.2%.

This percent error could have come from the fact that we used the sun to find the focal length of the lens, but it was a very gloomy day so taking the measurements of the focal length using the sun were not accurate.

Experiment 7: Introduction to Reflection and Refraction

The purpose of this lab was to study the properties of reflection and refraction using semicircular prism and a source of light.

In this experiment we used:

- Light box

- Semicircular prism

- Protractor

PART ONE:
First we adjusted the light box so that the light waves entered the flat part of the semicircular and exited the curved part. We taped a paper protractor under it so that the center of the flat side was on top of the protractor and on the 0 and 180 degree line. We then turned on the light box and recorded the angle of incidence θ1 and the angle of refraction θ2. We then rotated the prism  and protractor (together) by 4-8 degrees and measured the angles. We did this for a total of ten trials until we reached 80 degrees.  

 

Below is the data collected:

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of this graph was 1.9944. This slope is the index of refraction of the material that we used. 

PART TWO:

In this part of the experiment we did the same as above except that the light box ray entered the curve part of the semicircular prism and exited the plat side. We recorded the theta1 and theta2 when it was at 0 degrees and then rotated the prism every 4-8 degrees.

We recorded the values for theta1 and theta2 and found the sin(theta1) and sin(theta2). We then plotted the sin(theta1) vs sin(theta2). 

 The slope of the plot is 1.3346 is the index of refraction of the semicircular prism. We were not able to complete all of the trials because at 45 degrees, there was the critical angle where there was no refracted ray.

Conclusion:

The theoretical value for the the index of refraction of the semicircular prism is 1.49.

Experiment 6: Radiation Lab

The purpose of this experiment was to observe and study electromagnetic radiation using a simple antenna.

In this lab we used:
-Copper Wire
-Meter Stick
-BNC Connector
-Frequency Generator
-Oscilloscope

In the experiment, we created a transmitter by attaching a copper wire on to a meter stick using tape. One end was connected to the frequency generator. We then created a receiver by plugging in at the BNC connector into the oscilloscope. We then ran a 30 Hz frequency with a maximum amplitude. The time/div was changed to 01. ms and we decreased the voltage/div until we observed a signal on the screen. We then recorded the peak to peak amplitude of the electromagnetic wave for several trials.

Below is the data that was collected:

We then plotted the peak to peak amplitude as a function of distance:

CONCLUSION:
The graph was inverse proportional. We fitted the A/r and the A/r^2 to the graph. The A/r fit was better than the A/r^2 even though it is not a perfect fit. The best fit was A/r^n. We expected that the A/r function, but since it was not a point charge, we had to take into consideration the dx because the transmitter was linear perpendicular to the receiver.

Experiment 5: Introduction to Sound

The purpose of this lab was to observe the properties of sound waves using a human voice and a tuning fork.

We used:
- LabPro
- Microphone
- Brave student
- Tuning fork

PART ONE:
A brave student showed off his vocal skills by saying "AAAAAAAHHHHHH" smoothly into the microphone for 0.03 seconds. We recorded their beautiful voice and we saved the graph on LoggerPro. Below is the graph we obtained.

Below are the answers to the questions about the sound wave obtained.
a) The wave is periodic because although it is not a perfect sinusoidal wave, it has sinusoidal wave properties that repeat it self in a periodic manner.
b) There are about 4.8 waves in this sample. I determined it by counting the number of times the highest wave in the period appeared.
c)We recorded the sound for 0.03 seconds. This is similar to the amount of time that the brain takes to recognize a sound.
d)The period of this wave is about 0.00623 seconds. This is the time that we recorded the waves for, 0.03 sec, divided by the number of waves during that time, 4.8.
e)The frequency is 160 Hz. This is 1/T, where T is the period of the wave.
f) The wave length is lambda=v/f. This is equal to (340 m/s)/(160 Hz)= 2.125 m. This is about the distance from Professor Mason to the first row of desks in class when he is lecturing.
g)The amplitude is 1.543 arbitrary units. This was determined by the graph.
h)If we had recorded for 0.30 seconds, we would have a lower arbitrary amplitude, but besides that nothing else would change because the period of the wave is not changing.

The graph below shows how amplitude would change because it is an arbritary value if we recorded for 10 times longer.

PART TWO:

The individual wave patterns are similar because although they are not perfect sinusoidal waves, they are periodic. This wave has about 4.5 waves in 0.03 seconds. This means the frequency for this wave is   150 Hz. The period for each wave is about 0.0067 sec. The amplitude of this wave is 1.512 arbitrary units. The wavelength of this wave is 2.27 meters. The waves are similar in value but the first wave was a lot more smoother.

PART THREE:

Compared to the wave that was produced by a human's voice, the wave that was produced by the tuning fork is perfectly sinusoidal. It is much smoother and has a clear amplitude and frequency. There were 13 waves in 0.03 seconds. The period is 0.0023 seconds. The frequency was 433 Hz and the wavelength was 0.785 meters.


PART FOUR:

To produce a softer wave, we banged the tuning fork on a softer surface, such as the bottom of a shoe. What changed in this wave was that the amplitude of the wave was higher and that there were less waves produced in 0.03 seconds.