Hi, this is about thin film interference in ray optics. My book presents two similar problems, but somehow uses different paths for the same variable. I'll list out the given variables:

Question

--Problem A--

n1 < nf > n2, delta phase is therefore lambda over two.

Film thickness is 200 nm (L = 200 nm)

With nf = 1.40, find the dark spot in the visible range.

--Problem B--

n1 > nf < n2, delta phase is ditto

Film thickness is 380 nm (L = 380 nm)

with nf = 1.34, find the dark spot in the visible range.

--

The equation I am using is this,

Lambda = 2Lnf/m

Since we are trying to find a dark spot when the waves are already destructive, I thought there was no reason to use (m-1/2). In my head, using (m-1/2) will shift the phase another pi, creating constructive interference (and bright spots). So therefore, finding a dark spot in the visible range should use m = 1.

This method gave me the book's answer for problem A: 560 nm.

However, I got twice the amount for problem B. Now I hope I haven't lost my algebras yet, but even using (m-1/2) would actually yield quadruple the book's answer. The book says problem B's wavelength should be 509 nm, but I got 1,018 nm.

Am I missing something, or is the book wrong? This is very puzzling.

Indeed I did post this again. I'd rather have this cleared up then dwell on it.