Question

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:

--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.