Question

A scientist notices that an oil slick floating on water when viewed from above has many different rainbow colors reflecting off the surface. She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33.a. The index of refraction of the oil is 1.20. What is the minimum thickness t of the oil slick at that spot?b. Suppose the oil had an index of refraction of 1.50. What would the minimum thickness t be now?

Answer 1

Find the complete solution in the attachment

Answer 2

The minimum thickness t for each spot is;

A) 312.5 nm

A) 312.5 nmB) 125 nm

A) We are given;

Wavelength in air; λ = 750 nm

Index of refraction of the oil; η = 1.2

Using the condition for constructive inference, the formula for the oil slick at that spot is;

t_min = λ/(2η)

t_min = 750/(2 × 1.2)

t_min = 312.5 nm

B) We are told that the refraction index is now 1.5. Thus; η = 1.5

The formula for the oil slick at that spot will now be;

t_min = λ/(4η)

t_min = 750/(4 × 1.5)

t_min = 125 nm

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