Question

You are working as an expert witness for an attorney who is suing a shipping company. The company operates ships that carry crude oil across the oceans. One ship suffered an oil spill, in which the spilled oil spreads out into a slick, forming a thin film that f loats on the ocean surface. The legal issue is whether or not the ship spilled more or less than a volume of 10.0 m3 of oil into the ocean. You are reading documents that describe the oil slick on the ocean surface. In one doc-ument, you find out that ref lection tests were performed on the oil slick. These tests showed that the ocean surface showed a maximum of interference for 500-nm light over a circular area of radius 4.25 km surrounding the location at which the spill occurred. At distances farther from the loca-tion, the ocean surface showed no constructive interference, indicating that no oil was present. The type of oil involved has an index of refraction of n5 1.25. Determine for the attorney the minimum amount of oil that was spilled.

Answer 1

The refractive index of the oil is n = 1.25

The wavelength of the light = 500 nm

the radius of the affected location = 4.5 km = r

area of the affected location =

The formula for the constructive interference in case of oil layer is given by

considering the light is incident at an angle , we have

where d is the thickness of the oil layer

The volume of the oil =

This value of oil spread is within the limit.