The two different views of light, as a particle and as a wave, both contain insight and value. They have each enabled both new understanding of the natural world and the development and design of new technologies. Yet they appear to be vastly different in their conception of what light actually is. On the one hand, the particle model views light as a localized entity, a bundle of energy,that moves along a well-defined trajectory. On the other hand, the wave model describes light as a diffuse entity, permeating through space with no connection to the motion of solid things. How can these two pictures possibly refer to the same thing? This dilemma was recognized early on by Huygens and his contemporaries,but the two views remained in tension, as alternative descriptions of light, until the 19th century.
When Maxwell developed his theory of electromagnetic fields,he was able to use this to explain the properties of light as wave motion of those fields, as we saw in Chapter 3. This triumph of reasoning appeared to confirm the experiments of Thomas Young and Auguste Fresnel (described in Chapter 3) by providing an explanation of two fundamental phenomena, interference and diffraction, that did not easily fit within the particle model.Yet the concept of trajectories remained, and still remains, an extraordinarily powerful one for the analysis and design of optical systems. So there’s an uneasy truce of these two pictures—a dualism within classical physics—that requires some consideration.How can they be reconciled?
Looking at trajectories again
In the 17th century the Frenchman Pierre de Fermat proposed an ingenious formulation of refraction that was very different from that of Snell. Recall that Snell’s law deals with the change of direction of a ray of light at an interface between two transparent media. The ray, defined by the direction in which it is travelling towards the interface and the point at which it hits the interface,has its direction altered by an amount proportional to the ratio of the refractive indices of the two materials. It is only the local properties of the ray and interface that are important. Snell’s law applies at each point along the trajectory, as if the ray is‘feeling’ its way along, adjusting direction when it encounters a new interface.