Homework Help: How to determine M (Waves)

1. Feb 3, 2012

hyde2042

1. The problem statement, all variables and given/known data
http://i.imgur.com/xrba7.png

2. Relevant equations
I'm using this equation to find the thickness of the polymer.

[(m+(1/2)) λ = 2nt] (where "n" is the index of refraction and "t" is the thickness )

3. The attempt at a solution

I just want to know how m is determined. I've learned everything else, but I missed the first day on which m value to use and it's always jsut slipped my mind whenever I'm in class or lab.

2. Feb 3, 2012

ehild

m is any integer, including zero.

ehild

3. Feb 5, 2012

hyde2042

Thanks, but I'm still unsure as to why "0" is used in the solution instead of "1" or "2".

4. Feb 6, 2012

ehild

First: it is easier to make a thinner coating then a thick one.

Second: The reflectance depends on the wavelength, this function is about the form R=A+Bcos(4piND/lambda) (N is the refractive index, D the thickness). If the reflectance is zero at a specific wavelength, it stays low in the broadest wavelength range when D has the smallest possible value.
The figure shows the reflectance spectrum of two coatings, one 100 nm, the other 300 nm thick. Both have zero reflectance at 600 nm.

ehild

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