Understanding Thin Film Interference and Color Formation in Soap Films

[lockerman2007]

Consider a soap film where both sides of the film is air.
So reflected light has a π phase change.
Consider constructive interference,

2 d "nfilm" + 1/2λ = nλ , where "nfilm" is the refractive index of the film and d is the thickness the film.

Due to the gravity, the film at the bottom is thicker.
My teacher said that if the film is too thick, the above equation can be satisfied by more than one wavelength in the visible spectrum. So different colour combine to give a white colour.

I don't understand what is the meaning of this statement.
Is it mean that for different colour (λ), there will be a different order (n) to satisfy 2 d "nfilm" + 1/2λ ??

thank you!

 

[lpfr]

The interference is between the reflected ray at the first interface and the reflected ray at the second one.
As in any case there is a phase inversion (a phase change of pi radians) at one of the two reflections. Then if the path of light inside the film equals an integer number of wavelengths (in the film), the interference will be destructive. Is it is equal to an integer plus one half, the interference will be constructive.
Imagine that the film thickness is $$1000.5\lambda_1$$ (wavelengths in the film). What is the next value of $$\lambda$$ for which the interference will be constructive? It will be when the (same) thickness of the film is equal to $$999.5\lambda_2$$ and the next for $$998.5\lambda_3$$.
Compute the ratio between consecutive lambdas. You will realize that they are really close.

And in-between you have lambdas with destructive interference.

 

[sir-pinski]

Yes, that is correct. In thin film interference, the thickness of the film must be a certain multiple of the wavelength of the incident light in order for constructive interference to occur. This is represented by the equation 2d "nfilm" + 1/2λ = nλ, where "nfilm" is the refractive index of the film and d is the thickness of the film. So, for a given wavelength of light, there are multiple values of n that can satisfy this equation and result in constructive interference.

In the case of a soap film, the thickness can vary due to gravity causing the film to be thicker at the bottom. This means that for different parts of the film, there may be different values of n that satisfy the equation. This results in different wavelengths of light being reflected and interfering constructively, leading to the formation of different colors. However, if the film is too thick, there may be multiple values of n that satisfy the equation for a single wavelength of light, resulting in a combination of colors that gives a white appearance.

In summary, the statement means that the thickness of the film and the refractive index of the film can affect the colors observed in a soap film, and if the film is too thick, there may be a combination of colors that result in a white appearance.