Color and Spectra

In the experiment, we view the spectrum of colors and found in white light, and observed the effect colored filters have on the spectrum of white light. The purpose of this experiment is to find the wavelength of different color for the wavelength spectrum by applying the concept of constructive interference.

Equation for wavelength is:

λ= yd/R

λ is the wavelengh of the color on the spectruem, y is the width of the slit, d is the distance from the center to the first dark fridge, and R is the distance between the light source and the slits. In the experiment R^2=D^2+L^2 and y=D.

therefore, the equation for wavelength in the experiment is :

λ= Dd/sqr(D^2+L^2)




Part 1 White Light

Obtaining Wavelengh Uncertainty by plotting and get the slope.

Part 2 measure spectra of unknown#4 tube.

Distance of the diffraction grating d=2 μ meter

Distance from the bulb to to the grating D= 1.98 m

Y(m)         sinθ           λ                      calibrated

0.542        0.264024 5.28048E-07    5.33578E-07

0.606        0.29266   5.8532E-07       5.92534E-07

0.634        0.30495   6.099E-07         6.17837E-07

0.664        0.317951 6.35902E-07    6.44604E-07

0.736        0.348424 6.96848E-07    7.07342E-07

The spectrum of the #4 tube is not continuous and only some waves have strength range.

http://ioannis.virtualcomposer2000.com/spectroscope/elements

Professor announces the #4 is neno(Ne), and the spectrum range is similiar. However we confuse about the source color, for the photograph shows the source color is orange to red but the website give us white to gray. The white to gray color source color is Neptunium, but Np is radioactive element. We are not sure the problem coming from the bad camera to make the photo color change or something else.

Part 3. measure spectra of hydrogen.

Distance of the diffraction grating d=2 μ meter

Distance from the bulb to to the grating D= 1.98 m

Y(m)         sinθ           λ                      calibrated

0.4036      0.199731 3.99462E-07    4.0121E-07

0.487        0.238841 4.77682E-07    4.81731E-07

0.672        0.321388 6.42776E-07    6.5168E-07

The spectrum is not continuous and only few strength light.

By the formula of hydrogen, 1/λ= R(1/n^2-1/n'^2)

 R=1.0974*10^7

wave length        1/(λ*R)            n       n'      1/n^2-1/n'^2      error%

4.0121E-07       0.227123974   2       5       0.21                 8.154273

4.81731E-07    0.189160619   2       4       0.1875               0.885663

6.5168E-07       0.139830071   2       3       0.13888889      0.677651

The n'=5 part, if it change to n'=6, the error percent will reduce from 8 to 2%.

In the theroy, If the n=1, n'=infinite, wave length will be 91.127*10^-8 m

E= hc/wavelength= 2.18267*10^-18 J= 13.64eV

By our data, R as unknow n=2, n'=4, wavelength=4.81731E-07m

so we get R=11071185.7

If the n=1, n'=infinite, wave length will be 9.03246E-8

E=hc/wavelength= 2.20206*10^-18 J=13.7629eV

error= (13.7629-13.64)/13.64=0.9%

Conclusion

The spectra of the hydrogen approach the formula of hydrogen, 1/λ= R(1/n^2-1/n'^2).

The electron drop from different n and release the photon with different wave length.

The #4 tube is not hydrogen, so we may not use this formula of the hydrogen. Otherwise, the source color we photo is different from the website.

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.