Introduction to Vectors

Light has long captured the fascination of humankind and although we take phenomena such as reflection, refraction, diffraction and interference for granted, it is not hard to see why they posed perplexing problems throughout most of history. Why should light bend upon entering water? Why does light spread out after passing through a narrow gap? How does light travel to us from the sun, through the void of space? These sorts of questions have ensured that optics has a long and engaging history; mirrors were known to the ancients, eyeglasses were known by the thirteenth century, and, of course, the telescope was invented by Galileo around 1608.

The law of refraction was discovered by Willebrord Snell in 1621 and the phenomenon of diffraction was observed by both Francesco Maria Grimaldi and Robert Hooke by the mid-1600s. Sir Isaac Newton made great contributions to optics, proposing that 'white light' was a combination of all colors, and formulating a particle, or corpuscular, theory of light. At roughly the same time (the latter half of the seventeenth century), the Dutch physicist Christian Huygens proposed a powerful wave theory of light. As we shall discover, most of the history of optics is dominated by the debate over the nature of light: is light a particle or a wave, or is it something in between (a wavicle?)?

Another important figure in the history of optics is Thomas Young, an Englishman who revived the wave theory at the beginning of the nineteenth century by adding to it the principle of superposition. The French scientist Augustin Jean Fresnel, also an advocate of the wave theory, proposed a mechanistic description of light on the basis of it being a transverse oscillation through the ether, rather than a longitudinal one as had previously been assumed. The corpuscular theory seemed in very bad shape indeed. By 1845 Michael Faraday had performed several experiments showing that the plane of polarization could be altered by magnetic fields. This ultimately led to James Clerk Maxwell's brilliant unification of optics and electromagnetism, when his wave equations predicted that the speed of light should be 1/, which was remarkably close to the experimental value. Light, then, was an electromagnetic disturbance propagating through the ether.

As a wave, however, light must have a medium through which to propagate. Towards the end of the nineteenth century this medium, called the ether, became increasingly problematic; experiments by Michelson and Morley in particular could detect no motion of the ether relative to the earth. Such considerations led to Einstein's theory of special relativity and to the discarding of the idea of the ether altogether. Moreover, as the twentieth century progressed, quantum mechanics showed that all particles have a wavelike property; the distinction between waves and particles became less and less clear.

In this guide we will treat light usually as a wave, but sometimes as a particle, and as a general rule it is both or either. First, we will examine light as a wave, the relationship between light and electromagnetism, and gain some insight into how light interacts with matter. In the second topic, we will apply the laws of reflection and refraction to geometric optics. Finally, we will consider the important phenomena of interference, diffraction, and polarization.