Topic: LENSES
The reflection and refraction we have dealt with so far have focused only on light interacting with flat surfaces. Lenses and curved mirrors are optical instruments designed to focus light in predictable ways. While light striking a curved surface is more complicated than the flat surfaces we have looked at already, the principle is the same. Any given light ray only strikes an infinitesimally small portion of the lens or mirror, and this small portion taken by itself is roughly flat. As a result, we can still think of the normal as the line perpendicular to the tangent plane.
The four basic kinds of optical instruments—the only instruments are concave mirrors, convex mirrors, convex (or converging) lenses, and concave (or diverging) lenses. If you have trouble remembering the difference between concave and convex, remember that, like caves, concave mirrors and lenses curve inward. Convex lenses and mirrors bulge outward.
General Features of Mirrors and Lenses
Much of the vocabulary we deal with is the same for all four kinds of optical instruments. Before we look at the peculiarities of each, let’s look at some of the features they all share in common.
The diagram above shows a “ray tracing” image of a concave mirror, showing how a sample ray of light bounces off it. Though we will take this image as an example, the same principles and vocabulary apply to convex mirrors and to lenses as well.
The principal axis of a mirror or lens is a normal that typically runs through the center of the mirror or lens. The vertex, represented by V in the diagram, is the point where the principal axis intersects the mirror or lens.
Spherical mirrors have a center of curvature, represented by C in the diagram, which is the center of the sphere of which they are a slice. The radius of that sphere is called the radius of curvature, R.
All rays of light that run parallel to the principal axis will be reflected—or refracted in the case of lenses—through the same point, called the focal point, and denoted by F on the diagram. Conversely, a ray of light that passes through the focal point will be reflected parallel to the principal axis. The focal length, f,is defined as the distance between the vertex and the focal point. For spherical mirrors, the focal length is half the radius of curvature, f = R/2.
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