The given problem can be solved by using the condition for constructive interference.
To find the thickness of the oil slick, use the condition for constructive interference. Use the expression for the wavelength of ray in air medium and oil medium relation. The expression for the wavelength of ray in air medium and water medium relation can be used to solve the problem.
The condition for constructive interference can be expressed as,
Here, is the refractive index, is the order and is the wavelength of the radiation.
The light from air-oil interface has a phase reversal of . The light from oil-water interface has phase reversal of .
The interference between these two rays gives zero or two phases reversal.
For minimum thickness,
The expression for the minimum thickness can be expressed as,
The light from the oil water gives no phase reversal. The light from air-oil interface has a phase reversal of . The light from oil-water interface has no phase reversal.
The interference between these two rays gives phase reversal. The condition for constructive interference is given as,
Here, is the refractive index, is the order and is the wavelength of the radiation.
For minimum thickness,
The expression for minimum thickness can be expressed as,
The wavelength of ray in air medium and oil medium are related as follows as,
Here, is the refractive index of air and is the refractive index of oil.
(A)
The minimum thickness of the slick of the oil can be calculated as,
Substitute for and for in the expression for the minimum thickness of the slick of the slick of the oil.
(B)
The minimum thickness of the oil slick at the spot can be calculated as,
Substitute for and for in the expression for the minimum thickness of the slick of the slick of the oil.
(C)
The wavelength of light in the air can be calculated as,
The expression for wavelength of light in oil can be expressed as,
For longest wavelength ,
Substitute for in the thickness and wavelength relation.
Rearrange the equation to get the value of .
Substitute for , for , for in the expression of .
The wavelength of light in the water can be calculated as,
Rearrange the equation to get the value of wavelength of light in water.
Substitute for , for , for in the expression of .
Ans: Part A
The minimum thickness of the oil slick at the spot is .
Part BThe minimum thickness of the oil slick at the spot is .
Part CThe longest wavelength of light in water is .
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