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.)