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

[User1247]

Homework Statement

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."

Homework Equations

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.

 

[anathema]

Thank you for posting your question and providing your thoughts on the solution. I can understand your frustration in trying to find a clear answer to this problem. Thin film interference is a complex phenomenon and it can be challenging to understand.

Firstly, let's address the question itself. It asks which color one would expect to see near the bottom of a soap bubble, red or blue. To answer this, we need to consider the properties of the soap bubble, the incident light, and the viewing angle.

As you have correctly stated, the color we see in a soap bubble is a result of thin film interference. The film in this case is the soap bubble, which is essentially a thin layer of soap solution between two air layers. The thickness of this film is not uniform throughout the bubble, as gravity pulls the film downwards, causing it to become thicker at the bottom.

Now, let's consider the incident light. As you mentioned, the light source can be anywhere and the angle of incidence is not fixed. However, for the sake of simplicity, let's assume that the light source is directly above the bubble and the angle of incidence is 90 degrees.

In this scenario, the light rays will enter the bubble at the top and travel through the film until they reach the bottom. Now, as the light rays travel through the film, they undergo both reflection and refraction. The reflected rays will interfere with the incident rays, resulting in different colors being seen at different points on the bubble.

So, which color is most prominent near the bottom of the bubble? The answer lies in the wavelength of the incident light and the thickness of the film at the bottom of the bubble. Remember, the film thickness is not uniform and it is thicker at the bottom. As a result, the light rays that travel through this thicker part of the film will experience a longer path difference compared to the light rays that travel through the thinner part of the film. This path difference will result in a phase shift between the reflected and incident rays.

Now, let's consider the wavelength of the incident light. Red light has a longer wavelength than blue light. As a result, red light will experience a larger phase shift compared to blue light when traveling through the thicker part of the film. This means that red light will undergo more destructive interference compared to blue light, resulting in blue being the most prominent color near the bottom of the bubble.

In

 

[Moetasim]

Thank you for your thorough explanation and attempt at a solution. You are correct in your understanding that the color observed near the bottom of a soap bubble is due to thin film interference. However, the specific color observed depends on several factors such as the angle of incidence, film thickness, and light source. It is not possible to determine a specific color without knowing these variables. Therefore, it is not accurate to say that one color would be seen near the bottom of a soap bubble. The color observed would vary depending on the specific conditions of the bubble.