Light reflected from film, find maximum thickness of film, draw phase diagram.

[D.B0004]

Homework Statement

The light reflected from a soap bubble (n=1.4) appears bright red (wave length= 640 nm) at its center. What is the minimum thickness (in nm) there? Dray Phase Diagram.

Homework Equations

lambda(n)=lambda/n n=index of refraction
2*n*t=m*lambda
OR
2*n*t =(m+.5)*lambda
OR
2*n*t=m*lambda
I don't know which one to use.

The Attempt at a Solution

I tried skipping the first equation, because we know the light is INSIDE already, we should have the lambda(n) needed for the second three equations. I plugged numbers into both and got answers. 230 nm is what I believe the answer is.
I understand that each of these are for different situations of constructive vs. destructive interference, but I do not understand how to tell which situation is happening in this question! I do not know when to change m either!
Thanks so much for the help.

 

[anathema]

Thank you for your interest in this topic. I would like to offer some clarification and guidance on how to approach this question.

Firstly, it is important to understand that the equations you have listed are all related to the phenomenon of interference. Interference occurs when two or more waves interact with each other, resulting in a change in their amplitude (brightness) and/or wavelength. In the case of a soap bubble, the light is reflecting off both the outer and inner surfaces of the bubble, and these two reflected waves interfere with each other.

In order to determine the minimum thickness of the soap bubble, we need to use the equation 2nt = mλ, where n is the refractive index of the soap bubble (1.4 in this case), t is the thickness of the bubble, m is the order of the interference (1, 2, 3, etc.), and λ is the wavelength of the light (640 nm). This equation is used when the two waves are in phase, meaning that they are aligned in such a way that their peaks and troughs line up.

In this case, the light is reflecting off the inner surface of the bubble and then traveling back through the bubble to reach our eyes. This means that the wavelength of the light is effectively doubled (λ/2) when it reflects off the inner surface. So, we can rewrite the equation as 2nt = (m+0.5)λ. This equation is used when the two waves are out of phase, meaning that their peaks and troughs are misaligned.

Now, we need to determine the order of the interference (m) in order to solve for t. In this case, since the light appears bright red at the center of the bubble, we can assume that the interference is constructive. This means that the two waves are in phase and their amplitudes add together to produce a brighter light. So, we can use the first equation (2nt = mλ) to solve for t.

Plugging in the given values, we get:
2 * 1.4 * t = 1 * 640 nm
2.8t = 640 nm
t = 640 nm / 2.8 = 228.57 nm

So, the minimum thickness of the soap bubble at its center is 228.57 nm.

I hope this helps to clarify the situation and guide you in the right direction