# Thin film interference concept

Hello, I am having some difficulties understanding this concept. It seems like wikipedia and my notes/teacher contradict each other

According to my equation sheet, the equation for dark spots is 2nt = mλ and for bright spots is 2nt = (m + 0.5)λ. However, if a phase shift of 180 degrees occurs because the light hits something with a higher index of refraction (n), then the equation for dark spots and bright spots changes. If two phase shifts occur, they remain the same as if no phase shifts occur

Now I read wikipedia, and it seems to be the exact opposite of what is on my formula sheet. Am I reading this wrong, or which source is wrong?! I don't get it

http://en.wikipedia.org/wiki/Thin-film_interference

look at the articles about Soap bubble and anti-reflection coatings

Doc Al
Mentor
According to my equation sheet, the equation for dark spots is 2nt = mλ and for bright spots is 2nt = (m + 0.5)λ.
Seems backwards to me, assuming no phase shifts on reflection occur. The first gives the criteria for constructive interference and thus bright spots; the second, destructive interference and dark spots.

reading the textbook also confirms, it says ''in general, the condition for constructive interference in thin films is 2nt = (m + 0.5)λ. 24.9

This condition takes into account two factors (1) the difference in path length for the two rays and (2) the 180 degree phase change upon reflection.

If the extra distance 2t traveled by th ray 2 is a multiple of λn, the two waves combine out of phase and the result is destructive interference. The general equation for destructive interference in thin films is 2nt = mλ. 24.10

Equations 24.9 and 24.10 for constructive and destructive interference are valid when there is one one phase reversal.

So if I'm understanding this correctly, those equations are already assuming that it has undergone one phase shift? And if it undergoes 2 phase shifts, then the equations change?? My teacher did not make this clear at all, so I am really confused

Doc Al
Mentor
So if I'm understanding this correctly, those equations are already assuming that it has undergone one phase shift? And if it undergoes 2 phase shifts, then the equations change??
Yes. But rather than rely on rote memory, understand the principle. For destructive interference to take place, the net phase difference must be an odd multiple of λ/2. If a phase shift already gives you λ/2, then the thickness had better give you an integral multiple of λ to maintain the destructive interference.

What book are you using?

College physics by Serway. Also, I didn't comprehend your statement, particularly

''For destructive interference to take place, the net phase difference must be an odd multiple of λ/2. If a phase shift already gives you λ/2, then the thickness had better give you an integral multiple of λ to maintain the destructive interference.''

Doc Al
Mentor
You want the total net phase difference of the two reflections--due to the combination of phase shifts on reflection and the thickness of the film--to be an odd multiple of λ/2 for destructive interference. (And an integral multiple of λ for constructive interference.)

Does that make sense?

Here's a good discussion of thin film interference: Thin Film Reflection and Interference

the questions we always deal with either have 0, 1, or 2 phase changes. Does 0 and 2 phase changes share an equation and 1 phase change has its equation?

Doc Al
Mentor
Does 0 and 2 phase changes share an equation and 1 phase change has its equation?
Right. 0 and 2 phase changes end up with same equations, while a single phase change has different equations.

So to make this 100% clear so that there is no shadow of a doubt in my mind, this is how the equations look:

0 or 2 phase changes:
bright: 2nt = mλ
dark: 2nt = (m + 0.5)λ

1 phase change:
bright: 2nt = (m + 0.5)λ
dark: 2nt = mλ

jtbell
Mentor
Correct!

I still can't understand why the textbook/my teacher has to be so convoluted about explaining this. If someone just told me things straight up instead of eating around the bush, I probably wouldn't struggle so much in physics >_>