Light from * distant source
Bending of light rays at each surface of a convex spherical lens, showing that parallel light rays are focused to a focal point.
rays passing through each part of the lens will be bent exactly enough so that all the rays will pass through a single point, which is called the focal point.
Concave Lens Diverges Light Rays. Figure 49-3 shows the effect of a concave lens on parallel light rays. The rays that enter the center of the lens strike an interface that is perpendicular to the beam and, therefore, do not refract. The rays at the edge of the lens enter the lens ahead of the rays in the center. This is opposite to the effect in the convex lens, and it causes the peripheral light rays to diverge from the light rays that pass through the center of the lens. Thus, the concave lens diverges light rays, but the convex lens converges light rays.
Cylindrical Lens Bends Light Rays in Only One Plane—Comparison with Spherical Lenses. Figure 49-4 shows both a convex spherical lens and a convex cylindrical lens. Note that the cylindrical lens bends light rays from the two sides of the lens but not from the top or the bottom. That is, bending occurs in one plane but not the other. Thus, parallel light rays are bent to a focal line. Conversely, light rays that pass through the spherical lens are refracted
A, Point focus of parallel light rays by a spherical convex lens.
B, Line focus of parallel light rays by a cylindrical convex lens.
at all edges of the lens (in both planes) toward the central ray, and all the rays come to a focal point.
The cylindrical lens is well demonstrated by a test tube full of water. If the test tube is placed in a beam of sunlight and a piece of paper is brought progressively closer to the opposite side of the tube, a certain distance will be found at which the light rays come to a focal line. The spherical lens is demonstrated by an ordinary magnifying glass. If such a lens is placed in a beam of sunlight and a piece of paper is brought progressively closer to the lens, the light rays will impinge on a common focal point at an appropriate distance.
Concave cylindrical lenses diverge light rays in only one plane in the same manner that convex cylindrical lenses converge light rays in one plane.
Combination of Two Cylindrical Lenses at Right Angles Equals a Spherical Lens. Figure 49-5B shows two convex cylindrical lenses at right angles to each other. The vertical cylindrical lens converges the light rays that pass through the two sides of the lens, and the horizontal lens converges the top and bottom rays. Thus, all the light rays come to a single-point focus. In other words, two cylindrical lenses crossed at right angles to each other perform the same function as one spherical lens of the same refractive power.
A, Focusing of light from a point source to a line focus by a cylindrical lens. B, Two cylindrical convex lenses at right angles to each other, demonstrating that one lens converges light rays in one plane and the other lens converges light rays in the plane at a right angle. The two lenses combined give the same point focus as that obtained with a single spherical convex lens.
The distance beyond a convex lens at which parallel rays converge to a common focal point is called the focal length of the lens. The diagram at the top of Figure 49-6 demonstrates this focusing of parallel light rays.
In the middle diagram, the light rays that enter the convex lens are not parallel but are diverging because the origin of the light is a point source not far away from the lens itself. Because these rays are diverging outward from the point source, it can be seen from the diagram that they do not focus at the same distance away from the lens as do parallel rays. In other words, when rays of light that are already diverging enter a convex lens, the distance of focus on the other side of the lens is farther from the lens than is the focal length of the lens for parallel rays.
The bottom diagram of Figure 49-6 shows light rays that are diverging toward a convex lens that has far greater curvature than that of the other two lenses in the figure. In this diagram, the distance from the lens at which the light rays come to focus is exactly the same as that from the lens in the first diagram, in which the lens is less convex but the rays entering it are parallel. This demonstrates that both parallel rays and diverging rays can be focused at the same distance beyond a lens, provided the lens changes its convexity.
The relation of focal length of the lens, distance of the point source of light, and distance of focus is expressed by the following formula:
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