2 (25 points total) A disabled tanker leaks kerosene (n 1.20) into the Persian G

Question

2 (25 points total) A disabled tanker leaks kerosene (n 1.20) into the Persian Gulf creating a large slick on top of the water (n-1.30). a) (15 points) If you are looking straight down from an airplane, while the sun is overhead, at a region of the slick where its thickness is 460 Air nm, for which wavelength(s) of visible light in air (between 400 and 750 nm) is the reflection brightest because of constructive interference? For which wavelength(s) of visible light in air is the reflection dimmest because of destructive interference? So what color(s) will the slick appear to be? Show your work, and then indicate your answers below. Kerosene Water BRIGHTEST WAVELENGTHS DIMMEST WAVELENGTHS: APPARENT COLOR(S):

Explanation / Answer

nair=1

nkero=1.20

nwater=1.30

thickness=t=460x10^-9m

Brightest wavelenghts

Condition for constructive interference:

2d=(m)lambda/nkero....lambda=2d*nkero/m

for m=2, lambda=552nm. Other values of m yields in values of lambda that are out of the visible light range.

Dimmest Wavelenghts

Condition for destructive interference:

2d=(m+0.5)lambda/nkero....lambda=2d*nkero/(m+0.5)

for m=1, lambda=736nm and for m=2, lambda=441.6nm. Other values of m yields in values of lambda that are out of the visible light range.

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