Complete Question
An oil tanker has collided with a smaller vessel, resulting in an oil spill in a large, calm-water bay of the ocean. You are investigating the environmental effects of the accident and need to know the area of the spill. The tanker captain informs you that 18000 liters of oil have escaped and that the oil has an index of refraction of n = 1.1. The index of refraction of the ocean water is 1.33. From the deck of your ship you note that in the sunlight the oil slick appears to be blue. A spectroscope confirms that the dominant wavelength from the surface of the spill is 485 nm. Assuming a uniform thickness, what is the largest total area oil slick
Answer:
The largest total area of the oil slick [tex]A = 8.257 *10^{9} \ m^2[/tex]
Explanation:
From the question we are told that
The volume of oil the escaped is [tex]V = 18000 \ L[/tex]
The refractive index of oil is [tex]n_o = 1.1[/tex]
The refractive index of water is [tex]n_w = 1.33[/tex]
The wavelength of the light is [tex]\lambda = 485 \ nm = 485 * 10^{-9} \ m[/tex]
Generally the thickness of the oil for condition of constructive interference between the oil and the water is mathematically represented as
[tex]d = m *\frac{\lambda}{2n_w}[/tex]
Where is the order of interference of the light and it value ranges from 1, 2, 3,...n
It is usually take as 1 unless stated otherwise by the question
substituting value
[tex]d = 1 * \frac{485 *10^{-9}}{2 * 1.1}[/tex]
[tex]d = 218 nm[/tex]
The are can be mathematically evaluated as
[tex]A = \frac{V}{d}[/tex]
Substituting values
[tex]A = \frac{18000}{218*10^{-8}}[/tex]
[tex]A = 8.257 *10^{9} \ m^2[/tex]
