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.

Part A

The index of refraction of the oil is 1.20. What is the minimum thickness t of the oil slick at that spot?

Part B

Suppose the oil had an index of refraction of 1.50. What would the minimum thickness t be now?

Answer 1

whenever light refected from an optically denser medium , a sudden phase change of occurs.

Part A

Here light reflection takes place at air- oil boundary and oil- water boundary, At both places there is a phase change of . and

Path difference is

net phase difference between the rays of light is

For constructive interference

For minimum thickness, order of interference is one

Part B

Here light reflection takes place at air- oil boundary and oil- water boundary, but only at first reflection there is a phase change of . and

Path difference is

net phase difference between the rays of light is

For constructive interference

For minimum thickness, order of interference is zero