Light and Matter Waves

In this lab, we  use Vpython to visualize the wave fields. When light travels past an object or through an opening, it spreads out or diffracts. Every point on a wavefront can be considered as a source of secondary wavelets which spread out in all directions.With all the visualizations, it allows us to analyze how the electric changes when different wavelengths, or different separation between the two sources was adjusted.

The equation :

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

codes:

 

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

adding this code, each Eo will be the ouput

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()



Output the 3-D visualization of variable E between the source and the screen.



2mm wavelength                     
4mm wavelength                     
8mm wavelength

                    





Interference plots: 

For 2mm wavelength

                      
For 4mm wavelength                       
For 8mm wavelength                       Interference patterns are found when a double slit is presence. The wave is not a smooth round shape. 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 bigger separation between the two sources, the distances between the lines will  increase. The interference effect is reduced.




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


Intensity with smaller wavelength
Intensity with larger wavelength


The total intensity is zero at some points. With a decreased in intensity, the distance increases. With an increased in wavelength, the distances between the lines decrease.