Is one of the formulas used in "thin film" interference problems 2t = (m + 0.5)(lambda/n_film) OR 2t = (m - 0.5)(lambda/n_film), where t is the thickness of the film? I might have copied my notes down incorrectly in class, because according to internet sources, it is the latter but I have the former with the "+" in the brackets. So I just wanted to confirm the proper formula that I should be using. Thank you.
The point is that it differs by half a wavelength :)
So in the end, it doesn't really matter at all which one I use? Is there ANY difference that I'll get when solving for unknown values depending on which one I use?
That is right. You will get a different number of half waves inside there and it depends what you call m = 1 and m = 0. I would use the convention your teacher used.
If you use the + sign then m = 0 has half a wavelength in the film but if you start at m = 1 you want the - sign to get half a wave in there
To confirm the correct formula for thin film interference problems, we can start by discussing the concept. Thin film interference occurs when light waves reflect off both the top and bottom surfaces of a thin film, creating interference patterns.
The formula you are referring to is known as the "equation for film thickness" and it relates the thickness of the film (t) to the wavelength of light (λ), the refractive index of the film material (n_film), and an integer value (m) that represents the order of the interference pattern.
The correct formula for thin film interference is:
2t = (m + 0.5)(λ/n_film)
This equation represents a phase shift that occurs at the top surface of the film due to the reflection, resulting in an additional half-wavelength phase difference. The term (m + 0.5) accounts for this phase shift and determines the interference order.
So, based on your notes, the formula that you have written, 2t = (m + 0.5)(λ/n_film), is the correct formula for thin film interference problems.
It is important to note that there are variations of this formula depending on the specific circumstances or assumptions made. Therefore, it is always a good idea to consult your textbook or lecture notes for any specific variations that might have been discussed in class.
If you have additional questions or need further clarification, feel free to ask!