Thin film interference formulae

[khaos89]

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?

 

[Doc Al]

Why do you think you're wrong?

 

[khaos89]

Thank you for your answer, I think I am wrong because my book's solution is $t=\frac{m\lambda}{2n}$

 

[Doc Al]

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.)

 

[sardar]

Hello, it seems like you are on the right track, but there is a small error in your calculation. The correct formula for the thickness of the film in this case should be t=\frac{m\lambda}{2n}. This can be derived by setting \delta=(2m+1)\pi and solving for t. It is important to note that when using the destructive interference formula, the integer parameter m should always be an even number to ensure that the film thickness is a positive value. I hope this helps clarify your understanding of thin film interference formulae. Let me know if you have any further questions.