# Section 2: Measuring and Manipulating the Speed of Light

Interest in studying light, and in measuring its speed in different circumstances, has a long history. Back in the 1600s, Isaac Newton thought of light as consisting of material particles (corpuscles). But Thomas Young's experiments showed that light can interfere like merging ripples on a water surface. This vindicated Christiaan Huygens' earlier theory that light is a wave. Quantum mechanics has shown us that light has the properties of both a particle and a wave, as described in Unit 5.

Scientists originally believed that light travels infinitely fast. But in 1676, Ole Rømer discovered that the time elapsed between eclipses of Jupiter's moons was not constant. Instead, the period varied with the distance between Jupiter and the Earth. Rømer could explain this by assuming that the speed of light was finite. Based on observations by Michael Faraday, Hans Christian Ørsted, André-Marie Ampère, and many others in the 19th century, James Clerk Maxwell explained light as a wave of oscillating electric and magnetic fields that travels at the finite speed of 186,000 miles per second, in agreement with Rømer's observations.

Figure 3: The biker wins the race against the light pulse!

Experiments on the speed of light continued. Armand Hippolyte Fizeau was the first to determine the light speed in an Earth-based experiment by sending light through periodically spaced openings in a fast rotating wheel, then reflecting the light in a mirror placed almost 10 km away. When the wheel rotation was just right, the reflected light would again pass through a hole in the wheel. This allowed a measurement of the light speed. Fizeau's further experiments on the speed of light in flowing water, and other experiments with light by Augustin-Jean Fresnel, Albert Michelson, and Edward Morley, led Albert Einstein on the path to the theory of special relativity. The speed of light plays a special role in that theory, which states that particles and information can never move faster than the speed of light in a vacuum. In other words: the speed of light in a vacuum sets an absolute upper speed limit for everything.

## Bending light with glass: classical optics

The fact that light travels more slowly in glass than in air is the basis for all lenses, ranging from contact lenses that correct vision to the telephoto lenses used to photograph sporting events. The phenomenon of refraction, where the direction that a ray of light travels is changed at an interface between different materials, depends on the ratio of light's speed in the two media. This is the basis for Snell's Law, a relationship between the incoming and outgoing ray angles at the interface and the ratio of the indices of refraction of the two substances.

By adjusting the curvature of the interface between two materials, we can produce converging and diverging lenses that manipulate the trajectory of light rays through an optical system. The formation of a focused image, on a detector or on a screen, is a common application. In any cell phone, the camera has a small lens that exploits variation in the speed of light to make an image, for example.

If different colors of light move at different speeds in a complex optical system, the different colors don't traverse the same path. This gives rise to "chromatic aberration," where the different colors don't all come to the same focus. The difference in speed with a wavelength of light also allows a prism to take an incoming ray of white light that contains many colors and produce beams of different colors that emerge at different angles.

## Finding breaks in optical fibers: roundtrip timing

Figure 4: An optical time domain reflectometer in use.