![]() If you've ever noticed that a straw in a glass of water looks (from certain angles) like it is bent, or if you've ever seen a mirage on the road, then you've seen the effects of refraction. Refraction is a slightly less intuitive concept, but it has an effect on everyday life. If you've ever looked in a mirror, you've looked at light that has been reflected by a surface (the mirror). Reflection is just as you might imagine: rays of light that are deflected by a surface (perhaps being sent back toward their source) are reflected. Our study of geometrical optics will center on the application of two basic laws: one for reflection and one for refraction. (A condition of geometrical optics is that the wavelength of the light be much smaller than the objects it encounters.) Now that we have something of a physical idea of what a ray is, we can turn to the topic of geometrical optics, which is the study of electromagnetic waves that can be approximated using rays. Although these analogies are not necessarily incorrect, the above definition is slightly more mathematically rigorous in the context of classical electromagnetics. To be sure, it is sometimes easier to imagine a ray as, for instance, a "ray" of sunlight or a laser beam. This direction of travel, because it is uniform all across the plane wave, is called a ray. The diagram below shows a plane wave in two dimensions. For a so-called plane wave, all we need to know is the direction of travel, since the wave has a constant magnitude over the plane perpendicular to the direction. At a sufficiently large distance, the radius of the circle becomes so large that the wave appears (locally) as a line rather than a curve (in three dimensions, the wave appears to be a plane). Notice that as the waves get farther away from the source, the curvature of the circle decreases. The diagram below shows the waves moving outward from the source. ![]() The waves radiate symmetrically from the particle in concentric circles. Imagine electromagnetic radiation (light) emanating from a charged particle far away. O Use the law of refraction to describe the "bending" of rays as the pass from one material to another O Define the index of refraction and its relationship with material parameters O Use the law of reflection to calculate the direction of reflected rays O Describe the relationship between a wave and a ray In this article, we introduce the concept of a ray and discuss the laws of reflection and refraction.
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