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Chapter 32: Problem 2

Why does an oil slick show colored bands?

Short Answer

Expert verified
An oil slick displays various colored bands due to the phenomenon of thin-film interference. This occurs when sunlight reflects both from upper surface of the oil slick and from oil-water interface, resulting in the two light waves either reinforcing or canceling each other out. The varying thicknesses of the oil slick and varying angle of light incidence result in different colors being observed.

Step by step solution

01

Understand Interference

Interference involves the superposition of two waves resulting in a wave of greater, lower, or the same amplitude. In this case, consider two waves of light that have the same wavelength and are in phase with each other. If they meet, they will create a new wave with a higher amplitude due to constructive interference. However, if they are out of phase, they will cancel each other out, leading to destructive interference.
02

Understand Reflection and Refraction

When light hits the oil slick, a part of it is reflected off the top surface of the oil, while another part enters the oil and is reflected off the oil-water interface. The latter light wave experiences a phase change of 180 degrees because it reflects from a medium (water) with higher refractive index than the oil. This phase change is crucial to the interference pattern observed in an oil slick.
03

Calculate Path Difference

For the reflected light from the oil-water interface to constructively interfere with the light reflected from the top surface of the oil, it must travel an extra distance—back and forth within the oil layer—equal to a whole number of wavelengths.
04

Understand How Thickness Affects Color

The thickness of the oil slick at different points corresponds to different colors as various colors (wavelengths) of light constructively interfere at different thicknesses. If the oil slick is spread out and the sunlight strikes it at different angles, the observed color patterns will shift and change due to the changing path difference experienced by the light.

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Most popular questions from this chapter

Your molecular biology lab studies proteins, and you're frustrated because your microscopes can't quite resolve crystallized proteins. A sales rep touts the advantages of an expensive microscope using 200 -nm ultraviolet light, saying you'll be able to resolve structures less than half the size that's resolvable with your optical microscopes. Is the sales rep correct?

A double-slit system is used to measure the wavelength of light. The system has slit spacing \(d=15 \mu \mathrm{m}\) and slit-to-screen distance \(L=2.2 \mathrm{m} .\) If the \(m=1\) maximum in the interference pattern occurs \(7.1 \mathrm{cm}\) from screen center, what's the wavelength?

A double-slit experiment has slit spacing \(0.035 \mathrm{mm},\) slit-toscreen distance \(1.5 \mathrm{m},\) and wavelength \(500 \mathrm{nm} .\) What's the phase difference between two waves arriving at a point \(0.56 \mathrm{cm}\) from the center line?

You're investigating an oil spill for your state environmental protection agency. There's a thin film of oil on water, and you know its refractive index is \(n_{\text {oil }}=1.38 .\) You shine white light vertically on the oil, and use a spectrometer to determine that the most strongly reflected wavelength is \(580 \mathrm{nm}\). Assuming first-order thin-film interference, what do you report for the thickness of the oil slick?

Sketch roughly the diffraction pattern you would expect for light passing through a square hole a few wavelengths wide.
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