Experiment 15: LASER

Introduction
                   The purpose of this experiment is to understand how a laser works by investigating the difference between the spontaneous and stimulated emission. This experiment was conducted by using animations of light absorption and emission from a laser on Modern Physics website.
Clink here to go to "The Laser" page
Images

Figure 1: Absorption

 Figure 2: Spontaneous Emission

Figure 3: Stimulated Emission

Discussion
                  According to figure 1, it reveals that the number of photons (N_in) is equal to the addition of the number of photons out (N_out) and the number of electrons in the excited state (n₂). Specifically, 15=1+14. In addition, as shown in figure 2, the emission of photons from these excited states does not have a preferred direction, and the lifetime of each excited state is unpredictable. However, when a photon interacts with an excited electron, the emitted photons are in same direction, phase, and polarization. This is because the incident photon has the same frequency that the excited electron is needed to emit a photon. Therefore, the input of one photon stimulates the emission of another photon along with the incident photon as shown in figure 3. Therefore, the light is being amplified. In order to achieve a population inversion, where the number of excited atoms is more than that of the ground state atoms, the rate of pumping level has to be large enough so that the stimulated emission dominates. By changing the pumping level from 0 to 100, we found that the pumping level at least 70 is required to achieve this population inversion. If one of the photons are emitted in another direction, not aligned with the incident photon, it is possible that the photon is emitted spontaneously.

Experiment 14: Color and Spectra

Introduction

The purpose of this experiment was to understand how different elements only emit certain wavelengths and to identify an unknown element based on the wavelengths the element emits. This experiment hired the concept of the light ray diffraction. When a light source is shone through a slit, different colors with distinct wavelengths interfere constructively with each other, creating different colors at different positions. By knowing the distance between the light source and the color of interest, the wavelength of the interested color can be computed by using λ = Dd/L when the distance between the light source and the colored filter is very small compared to the slit. Alternatively, λ = Dd/√(L²+D²) can be used. The following image shows the derivation.  

Derivation of λ = Dd/√(L²+D²)

This experiment was conducted using a light source, colored filter, and two 1-meter sticks. The light source was shone to the colored filter which located 1 meter from the light source. Another 1 meter stick was located beside the colored filter in order to measure the distance of each color spectrum from the light source. The color spectrum was seen through the colored filter, and the distance between the light source and each type of color was recorded. A plot between the experimental and actual wavelength was constructed in order to made adjustment in further experimentation. A hydrogen light source was obtained, and the distance of each color from the light source was measured in same manner. Lastly, an unknown element light source was obtained to find the wavelength the element emits. The unknown element was identified based on the wavelengths.

Figure 1: The light spectrum from a white light source

Figure 2: The unknown light source (left) and the light spectrum from the unknown light source (right)

Figure 3: The light spectrum from a neon light source

Data and Analysis

Table 1: Wavelengths of visible light spectrum from a white light

Color	Range of the distance between the light source and the light spectra(cm)	Average distance(cm)	Average experimental wavelength(nm)	Average 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

Table 2: Wavelengths of visible light spectrum from a H­₂ light source

Color	Distance between the light source and the light spectra(cm)	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

Table 3: Wavelengths of visible light source from unknown #4 light source

Color	Distance between the light source and the light spectra(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

Graph 1: Experimental vs. Actual wavelength

Conclusion

                According to table 1, the experimental wavelengths were within the uncertainty of experimental errors, except the green spectrum. When the experimental vs. the actual wavelength was constructed as in graph 1, the relationship between the experimental and actual wavelength was obtained. This was used to obtain wavelengths that would be within visible range when spectrum from hydrogen and unknown light source were computed. As shown in table 2, the violet spectrum from the hydrogen gas was not within the range of visible light. After computing using the equation between the experimental and actual relationship, all of the wavelengths became within the visible range. Additionally, the adjusted wavelengths became within the uncertainty, except the yellow spectrum. This error was possibly contributed because the range of distinct color of light did not appear clearly. Hence, there were uncertainty in measurement of the distance between the light source and the color spectrum.          

                 Based on the wavelengths obtained from unknown light source as shown in table 3, the unknown gas #4 was identified to be neon gas since the peak wavelengths matched the neon spectrum most among the different elements in the periodic table. the neon light spectrum is shown in figure 3.   

Experiment 13: Light and Matter Waves

                        This experiment utilized programming in Vpython to see the light and matter waves behavior in 3 and 2 dimensions. The following is an example of the code used in Vpython to show desired 3 and 2 dimensional images.

__________________________________________________

from visual import *

import pylab as p

import mpl_toolkits.mplot3d.axes3d as p3

wavelength = 4.0e-3

scrnDist = 5.0e-2

scrnWdth = 2.4e-2

srceSepn= 2.4e-2

xs=[0,0]

ys=[-srceSepn/2,srceSepn/2]

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)

r1=sqrt((xd-xs[0])**2+(yd-ys[0])**2)

r2=sqrt((xd-xs[1])**2+(yd-ys[1])**2)

E0=A*cos(2*pi*r1/wavelength)/r1+A*cos(2*pi*r2/wavelength)/r2

#print E0

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')

fig2=p.figure()

p.contour(xd,yd,E0)

p.show()

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Images

Figure 1: 3D and 2D electric field plots created by a single light source at different wavelengths: 2mm, 4mm, and 8mm

(wavelength=2mm)

(wavelength=4mm)

(wavelength=8mm)

Based on these 3D and 2D plots, it shows that as the wavelength increases, the intensity becomes stronger, and the peaks of the wave become further apart. The circles on the 2D contour corresponds to the local peak intensity at a certain distance from the source.

Figure 2: 3D and 2D electric field plots created by 2 slits at different    wavelengths: 2mm, 4mm, and 8mm

 (wavelength=2mm)

(wavelength=4mm)

(wavelength=8mm)

(wavelength=4mm with doubled slit separation)

When there is a double slit, the peak intensities become 2 straight across the source. As mentioned previously, the intensity increases with increasing wavelength, but the peak of the intensity become broader at larger wavelength. In other words, the smaller the wavelength, the narrower the peak is. As the slit separation increases, the peaks intensity are further apart. 

                                  Figure 3: Comparison of intensity at different wavelengths

Shorter wavelength                              Longer wavelength

The above figures also show that when wavelength is smaller, the light intensity peaks are narrower than when the wavelength is larger. However, both cases have the same peak intensity. As the pattern moves away from the center, the intensity gets smaller since the interference becomes weaker. The intensity at some points along the screen is zero because the wavelengths interfere destructively at these points.