Measuring Plank's Constant

Relativity of Time and Length

Relativity of Time
 
Question 1: Distance traveled by the light pulse

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?

Answer 1: The distance travelled by the stationary clock is longer by a factor of gamma=1.41

Question 2: Time interval required for light pulse travel, as measured on the earth
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?

Answer 2: The time of the stationary clock is longer by (9.4 – 6.67)*10^-6 s = 2.73 *10^-6 s .

Question 3: Time interval required for light pulse travel, as measured on the light clock
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?

Answer 3: You observe a shorter distance and a longer time interval than the stationary observer.

Question 4: The effect of velocity on time dilation
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?

Answer 4: The difference in light pulse travel time will decrease.

Question 5: The time dilation formula
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.

Answer 5: (6.67*10^-6)(1.2) = 8.004*10^-6s

Question 6: The time dilation formula, one more time
If the time interval between departure and return of the light pulse is measured to be 7.45 µs by an earth-bound observer, what is the Lorentz factor of the light clock as it moves relative to the earth?

Answer 6:

7.45*10^-6 = (6.67*10^-6) γ

γ = 7.45/6.67

γ = 1.12

Relativity of Length

Question 1: Round-trip time interval, as measured on the light clock
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?

Answer 1: Yes, the moving light clock will experience a time interval longer than the stationary clock by a Lorentz factor.

 

Question 2: Round-trip time interval, as measured on the earth
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?

Answer 2: The round-trip time interval measured on the earth is longer by a Lorentz factor.

 

Question 3: Why does the moving light clock shrink?
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?

Answer 3:  Yes, since there is no length contraction the Lorentz factor is 1.

Question 4: The length contraction formula
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?

Answer 4: 1000m/1.3 = 769.23m


Conclusion
When objects move at speeds approaching the speed of light, length contracts and time dilates from the moving observer's perspective relative to a stationary observer's perspective.  

Polarization

Statement of Purpose
To observe the change of light intensity through a polarizer as a function of the polarizer's angle.

Procedure

Setup the polarizer to 0 degrees so that maximum intensity passes.

LoggerPro sensor is setup at the other end

Data

The curve is roughly the same as a cos^2 function.

This time an additional polarizer is placed

Interestingly, when two polarizers are 90 degrees with respect to each other which means that no light can pass through two such polarizers, but when a third mediating polarizer is placed in the middle the light is polarized by 45 degrees. When it passes through the last polarizer it changes by another 45 degrees, summing to a total of 90 degrees. This means that the the outgoing light is 0 degrees out of phase with respect to  

Conclusion
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, since the light that passes through the polarizer at all angles, the light can not be polarized

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

Yes, the polarizer is polarizing the light and decreasing the intensity of the light.

CD Diffraction

Statement of Purpose
Observe the diffraction of parallel light rays through multiple slits.

Procedure

Part 1
Set up the following

With given distance between slits in the diffraction grating, the target variable is the wavelength of the light. The distance from the Huygen sources to the screen is separated by one meter stick and the distance between maximas is measured by another meter stick.

The following calculation determined that the wavelength of the laser is (660 +- 27.6) nm which affirms the wavelength specified on the laser.

Part 2

With the given wavelength, this setup attempts to find the separation of the gratings on a compact disk (CD). The following measurements were made: the distance from the CD to the screen and the average distance between maximas.

Conclusion
The actual separation of the gratings in the CD is 1600 micrometers which compared to our experimental data makes an error of about 40.75%. This error comes from the angle at which we adjusted for the CD. A more accurate experiment would have the CD perfectly parallel to the screen.

Light Interference

Statement of Purpose
To measure the width of a hair using the two-slit interference principle.

Procedure

Set up the following.

The distance from the source to the screen was separated by one meter stick.

 

The average distance between two maximas were measured by a caliper. 

The control measurement of the hair was measured by a micrometer.

Data

Conclusion
According to CAQTI Cosmetics, Inc. the diameter of a typical black hair is between 56-181 micrometers which our experiment affirms.

Thin Lenses

Statement of Purpose
To observe the effects on light through a thin lense.

Procedure
Measure the focal length of the lense with two parallel rays.

The distance at which the two parallel rays converge is the focal length of the lense.

f = 5 +- 1cm

We focus light at a particular distance for several distances and measure the height of the object for which we used the tip of the arrow.

Data
d0 (± .1 cm) di (± .1 cm) h0 (± .1 cm) hi (± .1cm) M
5f = 25.000 7.000 1.800 0.400 0.23 ± 0.07
4f = 20.000 7.300 1.800 0.600 0.34 ± 0.07
3f = 15.000 8.200 1.800 0.700 0.39 ± 0.08
2f = 10.000 10.500 1.800 1.800 1.0 ± 0.1
1.5f =7.500 18.700 1.800 4.100 2.3 ± 0.2

 Object distance vs Image distance

Inverse Image Distance vs Negative Inverse Object Distance

Slope = .9475
y-intercept = .184

We see that at distances behind the focal length the virtual image reflects off of the back wall of the lense.

Conclusion
The y-intercept of the graph represents the 1/f in the lense maker's equation and since the slope is close to one we can write the equation of the graph.

y = x + (1/.184)

This equation relates the object distance vs the image distance.