Optics / interference in thin films

[johnj7]

Homework Statement

A soap bubble n=1.33 is floating in air. If the thickness of the bubble wall is 115 nm, what is the wavelength of the light that is most strongly reflected

Homework Equations

2nt=(m+0.5)(lambda)

The Attempt at a Solution

most strongly reflected = constructive interference
t=115 nm
lambda = unknown
n = 1.33
assumption m=0
plug and chug to get lambda

so I got the answer, but I was confused on why we make the assumption that m=0, couldn't m technically be any integer number? Do we just automatically assume that m=0 for "most strongly reflected" if a specific desired wavelength is not given?

thank you!

 

[mgb_phys]

Yes, strictly speaking the question should have said, what is the longest wavelength that is most strongly reflected.
However if you use m>0 you will get wavelengths that are outside the visible band.

 

[baba89]

As a scientist, it is important to carefully consider the assumptions that we make in our calculations. In this case, the assumption that m=0 is a reasonable one to make because we are looking for the wavelength of light that is most strongly reflected. This means that we are looking for the wavelength that produces the highest intensity of reflected light, which occurs when there is constructive interference. In order for there to be constructive interference, the path difference between the two reflected rays must be an integer multiple of the wavelength. By assuming that m=0, we are essentially saying that there is no additional path difference caused by multiple reflections within the thin film, and therefore the path difference is equal to the thickness of the film (t). If m were to be any non-zero integer, it would result in a larger path difference and therefore a different wavelength for constructive interference. In this case, m=0 is the most logical assumption to make in order to find the wavelength of light that is most strongly reflected.