The Digital Camera: Light Rays

At around 300 BC the great Greek mathematician Euclid of Alexandria published what we now understand to be an outlandish theory about the geometry of vision. Euclid believed that the eye projected several tiny rays outward in the shape of a cone and used those rays to sense – or “see” – the objects in their path. Many ancient scholars including Hero of Alexandria and Ptolemy refined Euclid’s naive theory, but it took more than 1000 years before scientists realized that the eye is a sensor for – not a source of – light. The useful concept of light rays, though, remained a staple in the theory of optics until the 1800’s when the English scientist, physiologist, linguist, and musician Thomas Young conducted experiments to demonstrate that light behaves like a wave. In the early 1900’s, Albert Einstein, Niels Bohr, and other modern physicists developed a more complete theory for light in which they claimed that light is made up of particles called photons, and that these photos behave at times like rays and at other times like waves.

Although the modern photon theory is more comprehensive, we can still use the ray theory to understand and anticipate the way light behaves in a wide range of situations. Optical engineers, for example, design sophisticated cameras by thinking of light as a collection of rays that bounce and bend as they propagate through the lenses and other optical elements in a camera. These designers envision a single ray much like the tightly-bound beam of colorful light that projects from a laser pointer. For large extended light sources like the sun, though, they imagine a countless number of these tiny rays extending in every possible direction.

The Properties of Light

Light possess three important characteristics that we can use to predict its behavior in optical systems.

First, light moves from one point to another with a speed that is determined by the surroundings in which it travels. In normal air, for instance, the speed of light is about 300 million meters per second, or about 670 million miles per hour. A ray of light from the sun, then, takes about eight and a half minutes to reach earth’s surface. As Douglas Adams reminds us in The Hitchhiker’s Guide to the Galaxy, “Nothing travels faster than the speed of light with the possible exception of bad news, which obeys its own special laws.”

Second, light travels slower when it is in water, glass, or some other surrounding than it does when it is in air. The speed of light in water, for instance, is about 225 million meters per second, or about three-fourths of its speed in normal air. The speed of light in glass is even slower at about 200 million meters per second, or about two-thirds of its speed in air. The ratio of the speed of light in air to the speed of light in a particular surrounding (like glass or water) is called the refractive index or index of refraction for the surrounding*. In general, the speed at which light travels in a medium depends on the color of the light, so the index of refraction for red light can be different than the index of refraction for green light which can be different than the index of refraction for blue light. Despite this dependence on color we often specify the refractive index as a single number that represents an average over the range of colors we expect to see. The average refractive index for water is roughly 4/3 (or about 1.33) which means that light is about 33% faster in air than it is in water. The average refractive index for common glass is approximately 3/2 (or 1.5) which means that light is about 50% faster in air than it is in glass. 

Finally, light travels from one point to another through a path that is faster than any of the nearby paths it might take. Because of this, light travels in a straight line between two points in the same surrounding, but, when traveling from air into glass or water, light may bend when it encounters the transition. Physicists and optical scientists call this phenomena the principle of least time, and they use this principle to design and analyze lens and other sophisticated optical elements.

In subsequent posts, we will use these principles to understand the important concepts of shadows, reflection, and refraction.

*To be precise, the index of refraction for a material or medium is the ratio of the speed of light in the medium to the speed of light in a perfect vacuum. But normal air has a refractive index of about 1.0003, so we often equate the speed of light in air with the speed of light in a vacuum.

© 2011 Timothy Schulz

The Digital Camera
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