Thin film interference formulae

AI Thread Summary
The discussion focuses on understanding thin film interference, specifically the conditions for destructive interference. The user is trying to derive the thickness formula for a thin film in air, initially arriving at t=(λ(m+1))/(2n) instead of the expected t=(mλ)/(2n). The confusion arises from the phase shift of π, which is accounted for in the calculations. Other participants clarify that both formulations are essentially equivalent, as adjusting the integer parameter m can reconcile the differences. The conversation emphasizes the importance of understanding phase shifts in thin film interference calculations.
khaos89
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Hello, I am trying to understand thin film (in air) interference but I have a problem:

I know we have destructive interference when \delta=(2m+1)\pi.

Now i can try to calculate the thickness of the film to get it, so

since \delta =\frac{4nt\pi}{\lambda} - \pi where t is the thickness,

I come to \delta=(2m+1)\pi=\frac{4nt\pi}{\lambda} - \pi

that leads me to t=\frac{\lambda(m+1)}{2n} instead of
t=\frac{m\lambda}{2n}

(n is the refractive index and m is the integer parameter)

Where am I wrong?
 
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Why do you think you're wrong?
 
Thank you for your answer, I think I am wrong because my book's solution is t=\frac{m\lambda}{2n}
 
khaos89 said:
Thank you for your answer, I think I am wrong because my book's solution is t=\frac{m\lambda}{2n}
The answers are essentially equivalent. (You can always start with m = -1 in your version.)
 
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