A scientist notices that an oil slick floating on water when viewed from above h

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. t = 312.5 nm

b. t = 125 nm

Now assume that the oil had a thickness of 200 nm and an index of refraction of 1.5. A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength ?water of the light in water that is transmitted most easily to the diver?

This is where I am stuck.

Explanation / Answer

Ans. For transmission of light, the same rules hold as before, only now one beam travels straight through the oil slick and into the water, while the other beam reflects twice (once off the oil-water interface and once again off the oil-air interface) before being finally transmitted to the water.

wavelength of the required light in air = 600 nm

There is a simple relationship between the wavelength of light in one medium (with one index of refraction ) and the wavelength in another medium (with a different index of refraction ):

y1n1 = y2n2 y represents wavelength

hence wavelength in water 451nm

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