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()

_________________________________________________

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.