Chapter 45: Problem 29

Question: A disabled tanker leaks kerosene (n = 1.20) into the Persian Gulf, creating a large slick on top of the water(n = 1.33).

1.

If you are looking straight down from an airplane onto the region of the slick where its thickness is $d~=~460~{\rm nm}$, for which wavelength(s) of visible light is the reflection the greatest?

2.

If you are skuba-diving directly under this same region of the slick, for which of the wavelengths of visible light is the transmitted intensity the strongest?

Solution: For the thin film, both interfaces correspond to the light moving from faster to slower medium, and so the reflected light suffers a $\Delta\phi~=~\pi$ at BOTH interfaces. Thus for the light reflected from both interfaces to be in phase (reflection maximum) means that the thickness must satisfy $2 n d~=~p\lambda$. Numerically, we find maxima at $\lambda~=~1104~{\rm nm}, 552~{\rm nm}, 368~{\rm nm}, ...$, and so in the visible region, we see $552~{\rm nm}$.

On the other hand, maximum transmission means minimum reflection (by energy conservation) and so looking up from the water, both reflections are from slower to faster medium, and hence there is no phase change at either interface. Thus for the light reflected from both interfaces to be out of phase (reflection minimum) means that the thickness must satisfy $2 n d~=~(p+{1\over 2}) \lambda$. Numerically, we find maxima at $\lambda~=~2208~{\rm nm}, 736~{\rm nm}, 441~{\rm nm}, ...$, and so in the visible region, we see $441~{\rm nm}$.