How Thin Must the Oil Film Be to Appear Red?

[matt85]

A thin film of oil (n = 1.49 is spread over a puddle of water (n = 1.33). In a region where the film looks red from directly above (lambda = 629 nm), what is the minimum possible thickness of the film?

______nm

Could someone please help me with this? I have no clue on this one, it was the only of the assignment I couldn't solve...

Thanks!

 

[Doc Al]

thin film interference

What conditions must be met so that the reflection from the top surface (air/oil interface) is exactly in phase with the reflection from the bottom surface (oil/water interface)?

 

[kyle8921]

I can help you with this question. The minimum possible thickness of the film can be calculated using the equation for thin film interference:

t = (m + 1/2) * lambda / (2 * n)

where t is the thickness of the film, m is the order of the interference, lambda is the wavelength of light, and n is the refractive index of the film.

In this case, m = 0 (since we are looking at the first order of interference), lambda = 629 nm, and n = 1.49. Plugging these values into the equation, we get:

t = (0 + 1/2) * 629 nm / (2 * 1.49) = 210.7 nm

Therefore, the minimum possible thickness of the film is 210.7 nm. I hope this helps you with your assignment!