Planck's Constant Activity

Objective

The objective of this experiment was to determine the value of planck's constant using the wavelength and voltage readings on LED lights.

blue LED:

Vo = 2.76 V
E = 4.42*10^-19 J
lambda = 450 nm

h = E*lambda/c = 6.62*10^-34

Yellow LED:

Vo = 1.95 V

E = 3.12*10^-19 J

lambda = 590 nm

h = 6.14*10^-34

Both of the experimental values of planck's constant agree with the theoretical value within 10% uncertainty.

Final Project: Holography

http://physicsholoproject.blogspot.com/

Color and Spectra Lab

Objective

Observe and measure the spectrum of colors found in white light and in single element tubes and analyze the relationship between wavelength and light diffraction through a grating.

Equipment

1) 2 Meter Sticks

2) White Light Source

3) Diffraction Grating

4) Discharge Tube and Power Supply

5) Hydrogen and Miscellaneous Tubes

Procedure

1) Set up the 2 meter sticks perpendicular to eachother on a table. Place a source of white light at the junction of the meter sticks. Place the diffraction grating at the other edge of the meter stick. Measure the distance between the light source and the diffraction grating. Look through the diffraction grating and record the apparent locations of each color on the other meter stick. Use these measurements and the diffraction grating equation to determine the wavelengths of the boundaries of each color.

2) Using the same set-up place the hydrogen discharge tube at the junction of the 2 meter sticks. Look through the diffraction grating and record the apparent positions of the bands of light created by the hydrogen light. Use the diffraction equation to determine the wavelengths of these bands.

 

3) Repeat the process in step 2 using an unknown discharge tube. After determining the wavelengths of the spectral bands try to figure out what the unknown element is using a database for elemental spectral lines.

Data and Calculations

White Light

using the measurements obtained in the photo above and the formula below we calculated the approximate border wavelengths for each color band.

D corresponds to the measured distance between the observed color band and the white light source.

lamda 1 corresponds to the far end of the blue color band and each subsequent wavelength corresponds to the next border of two color bands.

Hydrogen Gas

Above are the calculations for the spectral lines of hydrogen. The original wavelengths appear to be more correct than the adjusted wavelengths. This suggests that our calibration equation is inaccurate. Only 3 of the 4 visible wavelengths were observed due to the dimness of the hydrogen discharge tube.

Unknown Gas

Above are the calculations for the unknown discharge tubes. Again the original wavelengths seem more accurate than the adjusted wavelengths. We looked up a spectral line database for single elements and correctly guessed that our mystery element was Mercury.

Laser Active Physics Simulation

Question 1: Absorption
At any given time, the number of photons inputted into the cavity must be equal to the number that have passed through the cavity without exciting an atom plus the number still in the cavity plus the number of excited atoms. Verify this conservation law by stopping the simulation and counting photons.

- the sum of the photon output and number of excited atoms is always equal to the photon input.

Question 2: Direction of Spontaneous Emission
During spontaneous emission, does there appear to be a preferred direction in which the photons are emitted?

- there does not appear to be a preferred direction in which the photons are emitted

Question 3: Lifetime of Excited State
Does there appear to be a constant amount of time in which an atom remains in its excited state?

- there does not appear to be a constant amount of time for which the atoms are in an excited state. They appear to decay randomly

Question 4: Stimulated Emission
Carefully describe what happens when a photon interacts with an excited atom. Pay careful attention to the phase and direction of the subsequent photons. (Can you see why this is called stimulated emission?)

- when a photon interacts with an excited atom the atom emits a secondary photon in the same phase and direction as the initial photon

Question 5: PumpingApproximately what pumping level is required to achieve a population inversion? Remember, a population inversion is when the number of atoms in the excited state is at least as great as the number of atoms in the ground state.

- A population inversion occurs with a pumping level of about 70

Question 6: Photon Emission
Although most photons are emitted toward the right in the simulation, occasionally one is emitted in another direction. Are the photons emitted at odd directions the result of stimulated or spontaneous emission?

- the photons emitted at odd directions are usually the result of spontaneous emission, but can also be a result of stimulated emission if a spontaneously emitted photon interacts with another excited atom.

Relativity Active Physics Simulation

Objective:
Explore the relativity concepts of time and length dilation using active physics simulations.

Part I: 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 distance traveled by light on the moving clock was greater than that of the stationary clock

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 interval is longer on the moving clock

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, the light appears to travel the same distance

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?

the difference in light pulse travel time will decrease

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.

t = (gamma)(t) = 1.2(1000)/(3*10^8) = 4*10^-6 sec

6) 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?

gamma = t1/t2 = 7.45/3.333 = 2.235

Part II: 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?

this measurement does not depend on the movement of the clock

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?

longer

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

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?

1000/1.3 = 769 m

Light and Matter Waves

Objective

Use python programming to visualize and analyze light and matter wave functions in three dimensions

Equipment

1) Computer with python programming software installed

3D Plots

2 mm diffraction

2mm diffraction

4 mm diffraction

4 mm diffraction

4 mm interference

4 mm interference

8 mm interference

2d Plots

single slit diffraction

two slit interference

single slit diffraction

single slit diffraction

two slit interference 4 mm

two slit interference 8 mm

two slit interference 2 mm

Diffraction Pattern Cross Sections

single source

50 source, 500 detectors

larger view

smaller view



Diffraction Grating Lab

Objective

Determine the spacing of grooves on a compact disc using a laser and the laws of diffraction.

Equipment

1) cd

2) meterstick

3) helium neon laser

4) whiteboard

Procedure

Set up a cd and a whiteboard parallel to eachother. Shine the laser beam perpendicularly to the cd so that the primary reflected beam falls back onto the laser. Measure the distance between the two second order maxima. Also measure the distance from the cd to the whiteboard and the wavelength of the laser beam.

Data and Calculations

Measuring a Human Hair Lab

Objective: Determine the thickness of a human hair by observing the interference pattern created when a laser beam passes through a single strand of hair.

Lab Equipment: 


- index card
- strand of hair (at least one group member must not be bald)
- helium neon laser
- meter stick
- micrometer

Lab Procedure 


1) Punch a hole in the index card and tape the strand of hair across the hole. Make sure that the hair is straight.

2)  Clamp the card at least 1 meter away from a wall so that it is parallel to the wall.

3) Mount the laser so that the beam is perpendicular to the wall.

4) Adjust the card so that the beam falls directly on the hair. This should produce a diffraction pattern on the wall. Measure the distance between the card and the wall and the spacing between the 2 first order minima of the pattern.

5) Calculate the width of the hair using these measurements. Confirm this result using a micrometer.

Data:


distance between 2 first order maxima = 2y = 4.1 cm (error = 0.04 cm)
distance from card to wall = L = 180 cm (error = 0.5 cm)
wavelength of laser beam = lambda = 632.8 nm (error = 0.1 nm)

d*sin(theta) = m(lambda)

theta = arctan(2.05/180)

d = m(lambda)/sin(theta) ~ m(lambda)(L)/y = 55.5 micrometers (error = 0.73 micrometers)

Using the micrometer we found the width of the hair to be about 60 micrometers. This does not fall within our predicted interval. However, we had trouble figuring out how to use the micrometer and the discrepancy was most likely due to our inability to use the instrument.

Lenses Lab

Objective: Measure the properties of a converging lens observe the characteristics of images created by converging and diverging lenses.

Lab Equipment:

- Socket Lamp with V-shaped filament (filament is asterix-shaped)
- converging lens
- object (large hanging mass)
- masking tape
- lens holder
- large piece of cardboard (or other dark material)
- meter stick

Lab Procedure:

Part 1:

1) Obtain a converging lens and measure the focal length using a light source (the sun) located very long distance from the lens.
2) Place the lens in the lens holder on the table. position the lens holder about four focal lengths away from the filament. Move the cardboard screen in the path of the light which has passed through the lens. Move the cardboard screen back and forth until a sharp image occurs. Record the distance between each object and other observations specified in the lab manual.
3) Reverse the lens and note any changes in the image.
4) Repeat this process with the lens placed 2 focal distances and 1.5 focal distances away from the filament.

Data:

f = focal length, di = image distance, do = object distance, hi = image  height, ho = object height,
M = magnification = (hi)/(ho)
1) do = 60 cm, di = 21 cm, ho = 9 cm, hi = 3 cm, M = 0.333

The image is real and inverted.  When the lens is reversed all previous measurements of the image remain the same.

2) do = 30 cm, di = 31 cm, ho = 9 cm, hi = 9 cm M =1.00

 The image is real and inverted.  When the lens is reversed all previous measurements of the image remain the same.

3) do = 22.5 cm, di = 46 cm, ho = 9 cm, hi = 17.5 cm, M = 1.944

 The image is real and inverted.  When the lens is reversed all previous measurements of the image remain the same.

4) When half of the lens is covered in masking tape the image becomes much dimmer, but the shape and orientation of the image remain intact. We think that this occurs because every individual point on the lens projects the entire image out into the opposite side. covering any part of the lens will simply decrease the intensity of light going through.

Part 2:

1) Place a distinguishable object in front of a light source.
2) Using the same lens as in part 1, place the lens 5 focal lengths away from the object.
3) Measure the image distance, image height, and determine the type of image and its inversion.
4) Repeat for  a lens placed 4, 3, 2, and 1.5 focal lengths away from the object.

Data:

f = focal length, di = image distance, do = object distance, hi = image  height, ho = object height,
M = magnification = (hi)/(ho)

f = 15 cm

1) do = 75 cm, di = 18.5 cm, ho = 11.5 cm, hi = 2.5 cm, M = 0.217

2) do = 60 cm, di = 20 cm, ho = 11.5 cm, hi = 3 cm, M = 0.261

3) do = 45 cm, di = 22.5 cm, ho = 11.5 cm, hi = 4 cm, M = 0.348

4) do = 30 cm, di = 28 cm, ho = 11.5 cm, hi = 7 cm, M = 0.609

5) do = 22.5 cm, di = 35 cm, ho = 11.5 cm, hi = 10 cm, M = 0.870

in each of these trials the image was inverted and real.

when the object distance is decreased to a level below the focal length, the image is virtual and is not inverted.