ActivPhysics Lab - 18.3 The Laser

ActivPhysics Lab: 18.3 Atomic Physics: The Laser

Introducation:
The purpose of this experiment is to understand how does a laser works by investigating the difference between the spontaneous and stimulated emission.


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.

 Answer: The difference of photons in and out is the excited state atoms.


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

Answer:  During spontaneous emission, the amount of the photons out equals the amount of the atoms changed from excited state to ground state. Therefore, the photons are emitted have completely different directions and phases. 

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

Answer: There is no constant amount of time in which an atom remains in its excited state.

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. 

Answer: The amount of the photons out is the sum of the photons in and the atoms changed from excited state to ground state.

Question 5: Pumping


Approximately 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.

Answer: To achieve a population inversion, a pumping level 70 is required.

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?

Answer: In stimulated emission, the photons emits at an order direction; but in spontaneous emission, the photons emits at odd directions.

Experiment 13: Color And Spectra

Experiment 13: Color And Spectra

Introducation:
The purose of this experiment is to measure the spectral lines of white light source to identify the unknown gas. When a light source is shone through the slit creating different colors with distinct wavelengths which interfere constructively with each other. The wavelength of the interested color can be computed by using λ = Dd/L.

To begin the experiment, we first take a two meter long ruler and place it perpendicular to a one meter long ruler. Where the two ruler met we placed our light source. At the opposite end of two meter long ruler we placed our diffraction gradient. We were careful to make it so the light source sat right at the end of the ruler so that the diffraction gradient was exactly two meters away. We then made measurements where the visual spectrum laid along the one meter long ruler for the white light source. For the unknown gas we did the same except we noted where the spectral lines fell along the one meter long ruler and their color.

Data:
Part 1: White Light:

Hydrogen Tube:

Beacsue of our data did not match the accepted value for the color specturu, we use a graph to find out what factor that our data need to adjust. By using equation λ=λ'm + λ_0, we find out the factors that need to be adjust or shift.

Color	Distance between light source and spectre (m)	Experimental wavelength (m)	experimental wavelength (m)	Actual wavelength (m)
Violet	0.220	4.30*10^-7	4.41*10^-7	4.34*10^-7
Green	0.249	4.83*10^-7	4.92*10^-7	4.86*10^-7
Yellow	0.270	5.40*10^-7	5.45*10^-7	5.34*10^-7
Red	0.339	6.42*10^-7	6.42*10^-7	6.46*10^-7

Part 2: Unknown:

Color	Distance between light source and spectre (m)	Experimental wavelength (m)	Adjusted experimental wavelength (m)
Violet	0.197	3.87*10^-7	4.00*10^-7
Blue	0.220	4.30*10^-7	4.41*10^-7
Green	0.275	5.30*10^-7	5.36*10^-7
Orange	0.295	5.66*10^-7	5.70*10^-7

Conclusion
The different spectral lines indicate the different energy levels that the hydrogen can transition between. For each of these transitions, the hydrogen emits a photon corresponding to a specific wavelength. This method can be used to analyze an unknown gas and determine it's composition based on the energy levels. By using the same method the wavelengths and observed colors were noted, the unknown gas  most closely matched the emission spectrum of Hg.

ActivPhysics Lab- 17.2 Relativity of Length

17.2 Relativity of Length
In this activity we will learned how relativity distorts the length of objects as they approach the speed of light.

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:  If you are riding on the light clock, then in your frame of reference the light clock is not moving. If the light clock is stationary in your frame of reference, then the round-trip time interval is always the same. So the round trip time depends on whether the clock is stationary or moving.


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:  The round-trip time interval as measured by a timer on the light clock is the proper time interval between the departure and arrival of the light pulse. Therefore, the round-trip time will be measured to be shorter than the time measured relative to the earth.

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: Yes, in order to for the time intervals to obey the time-dilation relation, the length of moving light clock had to be small. And if the loreanzt factor is known and the time required for a moving clock to travel a given distance we can use the formula stated at the beginning of the activity to calculate the time required to reach the same distance relative to the stationary frame.

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?
Set the Lorentz factor to 1.3 and run the simulation to check your prediction.

Answer: The length of the light clock in the frame of reference of someone riding on the clock is termed the proper length of the clock. So we use the length is given by the proper length divided by the Lorentz factor. We obtain 1000/1.3 = 769 meters.

ActivPhysics Lab - 17.1 Relativity of Time

ActivPhysics Lab

17.1 Relativity of Time
This activity was used to help us understand the basic concepts of relativity. In these problems we will explore how space and time are distorted as different frames approach the speed of light.

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:
The distance traveled by the moving light clock is greater than the distance travel by the stationary light clock.


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: Since the speed of light is constant, the moving light clock must travel a further distance and therefore must take more time to complete one cycle.


Question 3: Time interval required for light pulse travel, as measured on the light clockImagine 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: In the moving frame of reference, the light pulse does not travel a greater distance, thus the time required for the light to make one cycle in the moving frame is the same time as the light to make one cycle in the stationary frame.


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: If the velocity of the light clock is reduced, the difference of the distance also decreased. Therefore, the difference of earth's timer and the light clock's timers also decreases.

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.

Set γ = 1.2 and run the simulation to check your prediction.

Answer: The time dilation of a moving clock with a Lorentz factor of 1.2 will have a time 1.2 times that of the original time.

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?

Since the Lorentz factor is the ratio of the earth-bound observor's time interval measurement to the proper time interval. Then ratio is 7.45 µs / 6.67 µs = 1.12.