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White light can be considered a mixture of three additive primary colors: red, green and blue. If the thickness of the soap film is just right to cause the destructive interference of one of the additive primaries, you will perceive a mixture of the two remaining colors: white - red = blue + green = cyan (bluish green) white - green = red + blue = magenta (reddish blue) white - blue = red + green = yellow Therefore, everywhere you see yellow, the film is just the right thickness to destructively remove the blue light waves. Where you see cyan, the red light has been destructively removed. And where you see magenta, the green light has been destructively removed.
This applet is a part of the final project for CS433 (instructor Peter Shirley), Spring Quater 1997
This applet simulates Thin Film Inerference in reflected light
Interference pattern of a thin, wedge- like film surrounded by air. The pattern is a series
of alternating dark and bright bands .
Placing a convex lens on top of a plane glass surface. The air between the two glasses varies in
thickness between zero and some value, and the thickness is angularly symmetric. The interference
produces circular fringes, with a bright spot in the center, first observed by Newton.
Variable thickness thin film is modeled by the smooth random potential. It is assumed that the
film is surrounded by air
Monochromatic light shined on the object,with wavelength
Red = 6.5E-7 m
Green =5.3E-7 m
Blue= 4.25E-7 m
White is a mixture of all three
|LEFT SLIDE BAR |
Changes the thickness of the film from 0.5E-6 m to 0.5E-7 m
|RIGHT SLIDE BAR|
Changes the brightness of the light source
Allows user to change the refractive index of the surrounding media (n1),film (n2) and substrate (n3),imitating diffrent materials.
|Index of Refraction|
|Diamond||n = 2.419|
|Glass||n = 1.666|
|Benzene||n = 1.501|
|Air||n = 1.000293|
How to Run:
To run the applet, choose one of the film shapes "Wedge","Lens", "Film1" or "Film2" and press the "Red", "Green","Blue" or "White" button. The applet will model interference in the chosen film under the applied light. One can stop painting at any time by pressing "Stop" and clear the screen using "Clear". User can vary thickness of the film by adjusting "Left Vertical Slide Bar" and simulate "sandwich" of different materials by changing the refraction indexes 'n1', 'n2' and 'n3' in the "Material" submenu. "Right Vertical Slide Bar" will change the brightness of the incident and therefore reflected light.
The brightness of the fringes strongly depends on indexes of refraction ( Fresnel Low), so after changing them, you may want to adjust the light brightness to get the most natural colors. If two or more indexes of refraction coinside, interference dissappears and one will see dark or bright screen.
|Tension fields in the film|
|Oil on the water|
Some Physics behind the Applet
Interference is a wave phenomenon and may only be described by wave optics . Two waves
of equal frequency in the same point
E1(k,x) = A1*cos(kx - wt + f1)
E2(k,x) = A2*cos(kx - wt + f2)
add up and the resulting wave will have the same frequency, w, but the amplitude will be
A^2 = A1^2 + A2^2 + 2*A1*A2*cos(f),
where f is the phase diffrence, f=f1-f2. If f does not change with time,then the waves are refered to as coherent. The intensity of the wave is I~ <A^2>(average over wave period). So, for the non-coherent waves, because f(t) randomly changes with time, average <cos(f(t))>= 0 and total intensity
I = I1 + I2.
But, if two waves are coherent,then
I = I1 + I2 + 2sqrt(I1*I2)*cos(f),
and at those points,where cos(f)>0, I will be greater than I1 + I2. For the points where cos(f) < 0, I will be smaller than I1 + I2. So, interaction of two coherent waves results in the spacial redistribution of the light flux; in some points it creates maxima and in others, minima of light intesity. This phenomenon is called interference.
It is difficult to observe intefernce of light from different sources, because of their
incoherence. But, one may obtain two coherent waves by splitting the light from the source
into two separate rays , making these rays cover diffrent optical paths and then combine
them together. The path differnce should not be vary large compared to the wave length to
This actually occurs alone in thin films such as thin layers of oil on water or soap bubbles. Part of the incident light reflects from the top surface of the film, and part refractes and goes inside the film, where it reflects from bottom of the film, goes outside, then interferes with the first one. Depending on the thicknes of the film, the two reflected waves will have differnt phases and add up either constructively or distructivly. The phase diffrence can be calculated by multiplying the path diffrenese d ( diffrence in the distances covered by two rays, in the case of the thin film and vertical light incidense it is just d=2*thickness of the film) by2*Pi*n/lambda,where lambda is the wave lenght of the incident light and n is a refractive index of the film.
f=2*Pi*n/lambda*(2*t) + (df1-df2),
and df1,df2 are the phases gained by both rays on reflection. When light goes from materials with lower index of refraction into materials with higher,the reflected ray changes its phase by Pi. For example, there will be Pi phase change in reflected ray, when light goes from air to water (n_air < n_water) and now change, when from water to air.
So,if the final phase diffrence f equals to Pi*n (where n-odd) than this spot will have minimum brightness, for f= 2*Pi*n (where n- integer)- maximum. When applying monochromatic light, the result would be dark and bright frindges of that color, whose position would be different for different colors. For white light (which is a combination of diffrent wavelengths) the result will be a colored pattern.