Experiment 16: Determining Planck's Constant

Introduction:
In this experiment, 4 different LEDs were used in order to make measurements to experimentally determine the value of Planck's constant, 6.626 * 10^-34 J*s.

Data:
Setup:

Power supply setup for LEDs

Initially, we measured the size of the continuous spectra and voltage of a yellow, red, blue, and green LED.



Yellow:

Yellow LED continuous spectra.

Red:

Red LED continuous spectra.

Blue:

Blue LED continuous spectra.

Voltmeter reading of 2.66V for blue LED.

Green:

Green LED continuous spectra.

Voltmeter reading of 2.82V for green LED.

Measurements made for LEDs.

A white LED was then investigated to see its continuous spectra and gather a voltage reading.

White:

White LED continuous spectra.

Voltmeter reading of 2.72V for white LED.

Calculations:

Calculations made for each LED.

Using the equation E=hf, where c=f*lambda, we can rewrite E=hf as lambda = hc/E. We notice that plotting our wavelength vs. voltage, we get our slope to be our experimental planck's constant value. 

Conclusion:
We notice that by graphing, we get a planck's constant value of 1.959 *10^-34, which gives us a percent error of 70.43%, but by calculating by hand, we get a planck's constant value of 6.849 * 10^-34, which gives us a percent error of 3.37%. This tells us that the use of more LEDs could give us much better results for an experimental planck's constant by graphical methods.

Experiment 15: Color and Spectra

Introduction: The purpose of this experiment was to measure the wavelength of light given off by a hydrogen gas spectra.

Data:
The experiment began by constructing an apparatus that allowed us to accurately measure the wavelengths of light emitted by our hydrogen gas source. We had to calibrate our apparatus using a white light source.

Setup of apparatus used for this experiment.

Light source used to calibrate our apparatus.

Calculations made for our calibration of the apparatus.

Calculations made for our apparatus.

The equation we found for our calibration of our apparatus was:

y=1.26x-145.56

This will allow us to accurately measure the wavelength of the hydrogen gas spectra.

Apparatus with hydrogen gas source instead of white light source used to calibrate the apparatus.

Apparatus with hydrogen gas source instead of white light source used to calibrate the apparatus.

A view of the spectra of the hydrogen gas.

Calculations made to measure the wavelengths of the hydrogen gas spectra using our equation found using the white light source.

Theoretical values for the wavelength of light emitted from hydrogen gas.

Conclusion:
We found that our apparatus gave us 6.40% error for the red wavelength, a 0.62% error for our blue wavelength, and a 1.71% error for our purple wavelength. This was within the accepted range of error, which means our measurements made were precise.

Experiment 13: Relativity of Time and Length

Relativity of Time

Question 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?

1. The distance is different by a factor of gamma.

Question 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 time is different by a value of 2.73 microseconds.

Question 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?

As a person riding on the light clock frame, there is no difference in the time interval.

Question 4: Will the difference  in the 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?

When the velocity is decreased, the system will become more classical and the difference between the timers will decrease.

Question 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 of 1.2.

Time = 8.004 microseconds

Question 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?

Lorentz factor value = 1.12

Relativity of Length

Question 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?

Yes, the light clock that is moving will experience a longer time interval than the light clock that is stationary relative to the earth.

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

Question 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?

Yes, the round-trip time interval could be equal due to the Lorentz factor of the length contraction equaling 1.

Question 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? 

The observers would measure a length of 769.2 meters.

Experiment 12: Polarization of Light

Introduction: The purpose of this experiment was to observe the change in light intensity of light passing through crossed polarizing filters and measuring the transmission of light through two polarizing filters as a function of the angle between their axes.

Preliminary Questions:

1) The view gradually fades and returns depending on the angle of the polarizer relative to the light incoming.

2) When the axes are parallel, the light intensity is at a maximum.

Data:

Example of measurement of light passing through the polarizers and measuring light intensity.

Setup of apparatus used in this experiment.

Another example of how measurements were taken.

Another view of the lab setup.

A third polarizer was added perpendicular to the first polarizer.

     Two polarizers:

Angle (degree)	Intensity (clockwise) (lux)	Intensity (counterclockwise) (lux)	Average (degree)	I/Imax	cos(theta)^2
0	204	208	206	1	1
10	201	198	199.5	0.968447	0.969846
20	189	182	185.5	0.900485	0.883022
30	172	163	167.5	0.813107	0.75
40	150	146	148	0.718447	0.586824
50	115	113	114	0.553398	0.413176
60	97	87	92	0.446602	0.25
70	83	75	79	0.383495	0.116978
80	67	63	65	0.315534	0.030154
90	59	57	58	0.281553	3.75E-33

           When the polarizers are perpendicular to each other, the amount of light that passed through the filter was minimal. When the polarizers are parallel to each other, the amount of light that passed through the filer was at a maximum.

     Three polarizers:

Angle (degree)	intensity (clockwise) (lux)	cos^2
0	50	1
10	49	0.969846
20	52	0.883022
30	58	0.75
40	62	0.586824
50	62	0.413176
60	58	0.25
70	54	0.116978
80	50	0.030154
90	48	3.75E-33

  

      When the second polarizer is at its 0 and 90 degree positions, the second polarizer is perpendicular to the either the first or third polarizer. The experiment is then similar to the perpendicular position in two polarizers. There is no light through the filter, so the intensity is at a minimum.
      When the second polarizer is at a 45 degree position, half of the light from the first filter goes through the second polarizer, and half of the light from the second filter goes through the third polarizer. Thus, the intensity is at a maximum.

Polarization upon reflection

Question 1: Does the light from the fluorescent bulb have any polarization to it? If so, in what plane is the light polarized? How can you tell?

No, the light from the fluorescent bulb does not have any polarization to it.

Question 2: Does the reflected light have an polarization to it? If so, in what plane is the light polarized? How can you tell?

Yes, the reflected light does have polarization to it. The light is polarized in the plane perpendicular to the table. When the polarizer was used to test the light, it has the most apparent change when it is parallel to the table.


Conclusion: The data measured in this experiment was consistent with the theoretical values.