A disabled tanker leaks kerosene ( n = 1.20) into the Persian Gulf, creating a l

Question

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) If you are looking straight down from an airplane, while the Sun is overhead, at a region of the slick where its thickness is 471 nm, for which wavelength(s) of visible light is the reflection brightest because of constructive interference? (b) If you are scuba diving directly under this same region of the slick, for which wavelength(s) of visible light is the transmitted intensity strongest?

Explanation / Answer

a) maxima determined by path difference

2L = m (lambda_n) = m*lambda / n2

lambda = n2 * 2L / m

= 2(1.2)(471 nm) / m

putting values 1, 2 and 3

1130.4nm , 565.2 nm, 376.8 nm

565.2nm is in visible range.

b) maxima in transmission <=> minima in reflection

2L = (2m +1) (lambda_n) / 2 = (2m +1)*lmbda / 2n2

lambda = 2n2*2L / (2m +1)

= 4(1.2)(471nm) /(2m +1)

putting m = 0, 1 , 2

lambda = 2260.8nm , 753.6nm , 452.16nm

ANd 452.16 nm is in visible range.

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