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.