Finding thickness of a thin film question

[feelau]

Homework Statement

A thin film of oil (n = 1.23) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, the film reflects most strongly red light at 640 nm and reflects no light at 569 nm. How thick is the oil film?

Homework Equations

2nt=(m+.5)*(wavelength)------constructive interference
2nt=m* wavelength------------destructive interference
n=index of refraction
t= thickness
m= order number

The Attempt at a Solution

So I tried to set the two equations together and using the corresponding wavelengths to solve for m. Next I just plugged m into one of the equations and using the corresponding wavelength to find t. Is that the correct method of doing this problem?

 

[G01]

I believe you have the formulas for constructive and destructive interference reversed somewhat. They should be:

Constructive: $$2nt = m\lambda$$

Destructive: $$2nt = (m-1/2)\lambda$$

 

[feelau]

Hm I think they are the same thing. My textbook says it's that way, the only difference is the 90 degree phase change. But would be method be correct?

 

[G01]

Yes, I guess they are both correct. Just in case you were wondering I looked up the formulas for thin films posted above in Knight's Physics book.(Not my favorite, but the only one I had on me.) Sorry for any confusion I may have caused.

 

[feelau]

np thanks for the verification