Relativity of Time and Length

Objective: The purpose of this experiment is to study the concept of Relativity of Time and Length. Different people in different frame of reference can feel the time, length of object, or velocity of events differently. For example, according to equation ∆t = γ∆t₀, observer who sees moving motion can feel a longer time than the person who is in a resting frame. For l=l₀ /γ
it states that the length measured by moving frame should be shorter than that measured by resting frame.

However, the relativity of time and length has to follow

Einstein’s Principle of Relativity

1.  The principle of relativity: The laws of physics must be the same in all inertial reference frames.

2.  The  constancy  of  the  speed  of  light:  The  speed  of  light  in  vacuum  has  the same value, c = 3.00 * 10⁸ m/s, in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light.

 v

γ = 1.20

 

 γ = 1.12             

          

 γ = 1.41

γ = 1.30

 

Conclusion

The time measured by the observer in moving frame is longer than that measured by the person in resting frame. This effect is called time dilation. Observers measure any clock to run slow if it moves relative to them. ∆t = γ∆t₀ With ∆t₀ represents the observer at rest in the same frame as the events. Besides the time difference, the distance between the two points is affected by different frame of reference. It is shown that the distance observed by moving frame is shorter than that observed by a resting frame, the proper length. This is called length contraction. This is consistent with the equation.When γ get larger, the speed increases. This is based on ratio u²/c2.  Also, the length, which is indicated by the blue line, measured by the resting frame is longer than that of moving frame, this is also consistent with the equation. However, only length parallel to the relative motion is affected by difference frame of reference. Lengths perpendicular to the relative motion is not affected.

 

Color and spectra

Objective: The purpose of this experiment is to collect  the wavelengths for certain gases and to identify an unknown gas. Different elements have their own and special wavelength. In this lab, students apply the concept of constructive interference and use the equation y=Lλ/d, with L is the length from light source to slit, y is the distance between the color of interest to the light source and d is the distance between slits. Student will measure the wavelength of a white light source using a straight filament light bulb first. Next, the wavelength measurements of hydrogen gas is taken. After that, student will measure the wavelength of unknown gas. Based on the wavelength the unknown element has, student has to identify it.



Figure 1: the set up of this experiment

Figure two, the color can be seen from the color filter.

Figure 3: unknown gas that has to be identified.

Data
 White light

Color	y	Average distance(cm)	experimental wavelength(nm)	actual wavelength(nm)
Violet	18.00-22.50 ± 0.50	20.25 ± 0.50	405 ± 10	415
Blue	22.50-24.20 ± 0.50	23.35 ± 0.50	467 ± 10	463
Green	24.20-27.50 ± 0.50	25.85 ± 0.50	517 ± 10	533
Yellow	27.50-30.00 ± 0.50	28.75 ± 0.50	575 ± 10	580
Red	30.00-38.50 ± 0.50	34.25 ± 0.50	685 ± 10	685

Hydrogen

Color	y	Experimental wavelength(nm)	Adjusted experimental wavelength(nm)	Actual wavelength(nm)
Violet	19.90 ± 0.50	398 ± 10	405 ± 23	410
Green	22.10 ± 0.50	442 ± 10	449 ± 23	434
Yellow	27.00 ± 0.50	540 ± 10	545 ± 23	486
Red	31.60 ± 0.50	632 ± 10	636 ± 23	656

Unknown gas

Color	Y(cm)	Experimental wavelength(nm)	Adjusted experimental wavelength(nm)
Violet	23.40 ± 0.50	468 ± 10	474 ± 23
Green	27.20 ± 0.50	544 ± 10	549 ± 23
Yellow	29.90 ± 0.50	598 ± 10	602 ± 23
Orange	31.10 ± 0.50	622 ± 10	626 ± 23
Red	33.00 ± 0.50	660 ± 10	663 ± 23

Conclusion: In the white light source, wavelengths of red, yellow, green, blue, and violent are measured. This is because white light is composed of all these colors. For hydrogen gas, four wavelength colors are recorded, they are violent, green, yellow, and red. This is because hydrogen gas only have these four colors. For the unknown gas, five colors of violent, green, yellow, orange, and red are seen and their wavelengths are collected. Based on the colors and wavelength, the unknown number 4 gas is determined to be neon. The actual color of neon gas is pink, blue, green, and red. Although some of the colors are hard to detected with naked eye, the result is quite accurate. The wavelength uncertainty is low, which means that this experiment can accurately measure the wavelength of the color emitted from the gas.

Laser

Objective: The purpose of this lab is to understand how laser works. Laser stands for "light amplification by the stimulated emission of radiation". Laser are commonly used in many ways, such as military applications, CD, reading bar code, and astronomy applications. The properties of laser are monochromatic, coherent, directional, and is highly focused. There are mainly three ways for lasers to move from one state to another. They are absorption, spontaneously emission,and stimulated emission.


Absorption



spontaneous emission


stimulated emission


Conclusion
Laser commonly use these ways to emit energy. In absorption, no photon is emitted. For the other two, photon is emitted.The first one is absorption. The atom is initially at ground state. If the atom absorb enough energy from a photon, it can be excited to a higher state. The amount of energy needed is E=hf=E(excited)-E(ground). No photon is emitted at the end.

The second one is spontaneous emission. This time, the atom is initially at excited state. However, no external energy from photon is received. So, the atom has to move by itself to ground state. Once it moves down to ground state, different from absorption, it will emit a photon. Again, the energy of photon emitted is E=hf. In this case, no external aid is provided, so the atom has to decline to ground state spontaneously to emit a photon. Therefore, it is called spontaneous emission
 
The third one is stimulated emission. This time, the atom is initially at excited state. But there is a external photon that provide energy of hf to stimulate the atom to ground state. (The atom no longer needs to move to ground state spontaneously.) When the external photon stimulates the atom to go to ground state, another photon, of same energy, phase, direction, and polarization, is emitted. The additional photon also has energy of hf. For stimulated emission, many photons are stimulated and emitted.
The favorable situation is there are more excited atom than ground state.

Experiment 13: Light and Matter Waves

Objective: The purpose of this experiment is to practice and develop the skill to use Vpython to visualize the wave fields. A 3D plot of xd and yd along the x- and y- axes and Eo along the z-axis is plotted. A 2D contour plot is plotted also to The value of wavelength is changed to observe the effect of wavelength on the locations of patterns. Besides, the intensity of the wave field is measured to observe the interference effects. 

Sample code used in this experiment:

from visual import *

import pylab as p

import mpl_toolkits.mplot3d.axes3d as p3

wavelength = 2.0e-3

scrnDist = 5.0e-2

scrnWdth = 2.4e-2

xs=0

ys=0

A=1

N=100

dX=scrnDist/N

Xcoords=arange(dX,scrnDist+2*dX,dX)

dY=scrnDist/N

Ycoords=arange(-scrnDist/2,scrnDist/2+2*dY,dY)

[xd,yd]=meshgrid(Xcoords,Ycoords)

r=sqrt((xd-xs)**2+(yd-ys)**2)

E0=A*cos(2*pi*r/wavelength)/r

#print E0

Add the following lines to obtain a visualization of the electric field through the space.

fig=p.figure()

Efield=p3.Axes3D(fig)

Efield.plot_wireframe(xd,yd,E0)

Efield.set_xlabel('Xd')

Efield.set_ylabel('Yd')

Efield.set_zlabel('E0')

p.show()

Add the following lines before the p.show command will show a 2D contour plot.

fig2=p.figure()

p.contour(xd,yd,E0)

3D plot                                                                  2D contour plot

 To investigate the values of the filed variable E between the source and the screen.

For 2mm wavelength

                    

For 4mm wavelength

                    

For 8mm wavelength

                                                                                                                                                                                            
From the above diagrams, it is shown that with an increased in wavelength, the wave field is less intense and more spread out. The results are expected. No interference pattern is observed since there is only one source. The wave is smooth and organized.


Interference: Situation when there is a small distance separate two point.

For 2mm wavelength

                     

For 4mm wavelength

                      

For 8mm wavelength

                      

From the above diagrams, two peaks are observed on the 3-D plot. Interference patterns are found when a double slit is presence. The wave is not a smooth round shape anymore. With an increased wavelength, the wave field is less intense and more spread out. 

The separation between the two sources was changed to 24mm

                         

With an increased in the separation between the two sources, the distances between the lines increased. The interference effect is reduced.

Intensity of the wave field was measured to observe the interference effects.

Intensity with larger wavelength

As shown on the diagrams, the total intensity is zero at some points. The heights of the maximums change as I go away from the center. With a decreased in intensity, the distance increases. With an increased in wavelength, the distances between the lines decrease.