Constructive interferance homework (concept) help

1. Dec 7, 2016

Rae__

Problem:
Consider a 360-nm thick oil film floating on the surface of the water. The indices of refraction of the oil and water are 1.5 and 1.33. The surface of the oil is illuminated from above at normal incidence with white light. (A) Find the shortest wavelength of light in the 400nm to 800 nm wavelength band that is strongly reflected.
(B) Find the longest wavelength of light in the 400nm to 800 nm wavelength band that is strongly reflected.

Relevant equations:

2t = (m+0.5)lambda (m=0,1,2...) This eq is for constructive reflection when one of the waves is phase shifted (the reflection from the air-->oil interface should have a phase shift, but that is all.)

I am slightly confused on equations. In online forums it might say "nt=(m+0.5)lambda" but my textbook gives that equation.

My work so far:
I arranged the equation I have seen online to be lambda()=(tn)/(m+0.5)
Then I plugged in m=0,1,2...
I got from 0 to 2: 1080nm, 360nm, 216.
*when you use the equation with the n, you get the right answers

I am overall confused. I don't get the right answer, the longest wavelength of light should be 720. I would appreciate any help in the right direction.

Last edited: Dec 7, 2016
2. Dec 7, 2016

Rae__

My error was forgetting that wavelengths have DIFFERENT LENGTHS IN DIFFERENT MATERIALS AND I DIDNT EVEN FACTOR THAT INTO the equation, so I was missing lambda (in material) = lambda/n.