# PHYS 2212 Module 15

15: Interference

Soap bubbles are blown from clear fluid into very thin films. The colors we see are not due to any pigmentation but are the result of light interference, which enhances specific wavelengths for a given thickness of the film.

The most certain indication of a wave is interference. This wave characteristic is most prominent when the wave interacts with an object that is not large compared with the wavelength. Interference is observed for water waves, sound waves, light waves, and, in fact, all types of waves.

If you have ever looked at the reds, blues, and greens in a sunlit soap bubble and wondered how straw-colored soapy water could produce them, you have hit upon one of the many phenomena that can only be explained by the wave character of light (see Figure 3.1). The same is true for the colors seen in an oil slick or in the light reflected from a DVD disc. These and other interesting phenomena cannot be explained fully by geometric optics. In these cases, light interacts with objects and exhibits wave characteristics. The branch of optics that considers the behavior of light when it exhibits wave characteristics is called wave optics (sometimes called physical optics). It is the topic of this module.

It’s our last module of the semester! In this module, we will discuss the wave model for light. You will need to remember some things from PHYS 2211 having to do with waves, but I will review them briefly, too. The most important thing to remember is wave interference, when waves overlap and interfere constructively (combine to make a bigger wave) or destructively (combine to make a smaller wave). This is property of waves, only. Think about it – can you add two particles together to get a smaller particle, or no particle?

As long ago as the 17th century, there were two competing models to describe the nature of light. Isaac Newton believed that light was composed of particles, whereas Christopher Huygens viewed light as a series of waves. Both models could explain reflection and refraction, but the phenomena of diffraction and interference could be more easily explained by Huygens’ wave model. In the early 19th century, Thomas Young’s double-slit experiment provided evidence that supported the wave nature of light.

Electromagnetic radiation propagates as a wave, and as such can exhibit interference and diffraction. This is most strikingly seen with laser light, where light shining on a screen looks speckled (with light and dark spots) rather than evenly illuminated, and where light shining through a small hole makes a pattern of bright and dark spots rather than the single spot you might expect from your everyday experiences with light.

#### 15.1 Young’s Double-Slit Interference

• Explain the phenomenon of interference
• Define constructive and destructive interference for a double slit

#### 15.2 Mathematics of Interference

• Determine the angles for bright and dark fringes for double slit interference
• Calculate the positions of bright fringes on a screen

#### 15.3 Multiple-Slit Interference

• Describe the locations and intensities of secondary maxima for multiple-slit interference

#### 15.4 Interference in Thin Films

• Describe the phase changes that occur upon reflection
• Describe fringes established by reflected rays of a common source
• Explain the appearance of colors in thin films

#### 15.5 The Michelson Interferometer

• Explain changes in fringes observed with a Michelson interferometer caused by mirror movements
• Explain changes in fringes observed with a Michelson interferometer caused by changes in medium