Homework Help: Bubble Optics - Which colour would I see near the bottom?

1. Jan 26, 2008

User1247

1. The problem statement, all variables and given/known data
Hi everyone, I'm having trouble finding anything in the way of information on this problem. If anyone can help I'd appreciate it. I got a couple answers on yahoo answers but nobody could give an explanation for their answer. I want to understand where the answer comes from so that I can learn.

"Which of the following colours would you expect to see near the bottom of a soap bubble, red or blue? Justify your answer."

2. Relevant equations

3. The attempt at a solution

Ok here's what I know about the solution:

-It's a thin film interference problem, the incident ray, i1, strikes the outer layer of the bubble and splits into two; r1 reflects immediately off the surface and heads off, r2 transmits through the thickness of the bubble film and reflects off the inner surface and heads off alongside r1
-r1 and r2 are now out of phase because of the path difference ,λ', the extra distance that it had to go compared to r1
-r1 and r2 have wavelength λ, the two waves interfere, depending on the phase shift they could interfere constructively or destructively
-the phase shift depends on the path difference, the wavelength
-the path difference depends on the angle of incidence and the film thickness
-the bottom of the bubble will be thicker because gravity is pulling the soapy film downwards
-thin film interference only works when the film thickness is a few wavelengths at most

So, the colour that is most prominent at some part on a bubble is the one whose wavelength is the right length to give the most constructive interference with the film thickness on that part of the bubble with that angle of incidence for the light illuminating the bubble.

By my estimation, any colour could be most prominent at any part of the bubble, it all depends on the angle of incidence and thickness of the bubble. I don't see that I can come up with any reasonable argument to say that the bottom of a bubble is associated with a particular angle of incidence, the light source could be anywhere, the bubble could be above the viewer or below.

Just saying that the bottom of the bubble is thicker doesn't help either, allowing the film thickness to vary and fixing all other variables, we could start with say, negligibly small phase shift and increase it through several wavelengths until the effect washes out by the film being too thick. As the film thickness and path difference increase through 0nm to say 2500nm the most prominent colour would cycle through the spectrum a few times. So I can't see that a thicker film would favour a particular colour either.

I'm lost on this one and I'm trying hard to come up with an answer.
Thanks.