When a thin soap ﬁlm is very thin, we see it as black. How thick (in nm) is the ﬁlm
in the region where we see the ﬁrst red band? Take the wavelength of red light to be 752
nm and the index of refraction of the soap to be n = 1.33.
[2nt/λ] - 1/2 = m
The Attempt at a Solution
Solving for t:
First with m = 1 I moved the 1/2 over to get 3/2, Then I multiplied 3/2 by the wavelength 752e-9 and divided this result by 2n, n being 1.33.
The answer I attained after solving for t was: 424 nm.
The correct answer is 141 nm.
I still don't know what I'm doing wrong here. I have noticed that if I divide my answer by 3 I get the correct answer, though this may just be coincidence.
Also if anyone is using Walker edition 4, on page 988 the practice problem seems to be this exact same scenario and I am having the exact same problem.