A disabled tanker leaks kerosene ( n = 1.20) into thePersian Gulf, creating a la

Question

A disabled tanker leaks kerosene (n = 1.20) into thePersian Gulf, creating a large slick on top of the water(n = 1.30). (a) If you arelooking straight down from an airplane, while the Sun is overhead,what is the thickness at a region of the slick where the reflectionis brightest for visible light with wavelength 681nm? (b) If you are scuba diving directlythe slick, what is the thickness for which light with wavelength547 nm is transmitted strongest?

Explanation / Answer

Given that for air n1 = 1      keosene n2 = 1.20      water n3 = 1.30       L = 681 nm (a)          The path lengthbetween two rays = 2L          For constructiveinterference                   2L = m / n2         ==> =2Ln2 / m                   = 2 * 681 * x10-9 * 1.20 / 1 = 1634.4 nm m = 2               = 817.2 nm m = 3               = 544.8 nm        Therefore 544.8 nm wavelength falls in the visible region. b)          For kerosene -water interface                 2L = (m + 1/2) / n2         ==:> =4n2L / (2m+1) For m = 1                  = 4 * 1.2 * 681nm / (3)            = 1089 nm m = 2     = 653.7 nm m = 3    = 466.9 nm Therefore 466.9 nm falls in the visible region.

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