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.