Oil & Water Film: Min Thickness of 313nm

[xamy]

Homework Statement

A thin film of oil (n = 1.50) is spread over a puddle of water (n = 1.33). In a region where the film looks red from directly above (λ = 626 nm), what is the minimum possible thickness of the film?

Homework Equations

2nt = (m+0.5)λ
t = (m+0.5)λ/2n

The Attempt at a Solution

t = (1+0.5)(626E-9m)/2(1.50)
t = 313 nm

Anyone please correct the solution.

 

[TSny]

You are looking for the minimum thickness. Did you choose the correct value of the integer m to get the minimum thickness?

 

[xamy]

I think it should be zero

 

[TSny]

Right.

 

[xamy]

thanks

 

[xamy]

Homework Statement

A camera lens (n = 1.29) is coated with a thin film of magnesium fluoride (n = 1.71) of thickness 87.0 nm. What wavelength in the visible spectrum is most strongly transmitted through the film?

Homework Equations

2nt = mλ
λ = 2nt/m

The Attempt at a Solution

λ = 2(1.71)(87E-9m)/(1)
= 297.54 nm

Solution is not correct.

 

[Doc Al]

You failed to consider possible phase changes upon reflection.

 

[TSny]

I think you have the phase change due to reflection accounted for. (You want maximum transmission and hence minimum reflection.) But is your answer in the visible part of the spectrum?

 

[xamy]

No its not

 

[TSny]

I might be overlooking something, but it doesn't appear to me that you can get an answer in the visible spectrum.

 

[Doc Al]

I think you have the phase change due to reflection accounted for.

D'oh! You're right.

 

[berkeman]

Oops, I merged the two threads after receiving a report that they were duplicate threads. I see now that they have slight differences in the problem statements. Sorry about that!

 

[TSny]

A web search indicates that magnesium fluoride has an index of refraction of about 1.4. Glass (camera lens) is usually about 1.5. For these values you can get an answer in the visible.

 

[Doc Al]

Looks like the problem statement (for the visible light question) was mistaken. Where is the problem from?