The law of reflection tells us that ? 2 = ? 3 on the basis of this and our conclusion about the relationship of ? 1 and ? 3, we can express ? 2 in terms of ? 1 as follows. Let's add angle ? 3 to the figure note that this angle is 90° - ? 1. The normal line is shown as the dashed line in the figure.
Solution: The law of reflection states that the angle of incidence is equal to the angle of reflection (where both angles are measured from the normal line to the surface). Practice Problem: A ray is incident on a mirror as shown below, where the dashed line is normal to the surface. Several normal lines are shown for different points on the curved surface below. Nevertheless, the same principle applies: the normal line is the line perpendicular to the surface at the point of incidence. Although this is easy for a flat surface (it is just the line that is perpendicular to the surface), it is slightly more complicated for curved surfaces. The law of reflection states that the angle of incidence is equal to the angle of reflection, or, stated mathematically,Īlthough this relation is simple, you must always be careful to find the correct normal line that intersects the point of incidence. The angle ? r for the reflected ray is called the angle of reflection. Concomitantly, the angle ? i that the incoming ray makes with a line (dashed in the diagram) normal to the surface is called the angle of incidence. We identify the incoming ray as the incident ray and the outgoing ray as the reflected ray. Interested in learning more? Why not take an online Physics course?įirst, we consider reflection, as shown in the diagram below for a light wave striking a surface. Two very simple formulas govern reflection and refraction in geometrical optics. Refraction is the "bending" of light rays resulting from changes in the characteristics of the medium through which the rays are traveling. 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
\): Total internal reflection for light traveling from glass to air.In this article, we introduce the concept of a ray and discuss the laws of reflection and refraction.
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