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Figure 49-7

A, Two point sources of light focused at two separate points on opposite sides of the lens. B, Formation of an image by a convex spherical lens.

Formation of an Image by a Convex Lens

Figure 49-7A shows a convex lens with two point sources of light to the left. Because light rays pass through the center of a convex lens without being refracted in either direction, the light rays from each point source of light are shown to come to a point focus on the opposite side of the lens directly in line with the point source and the center of the lens.

Any object in front of the lens is, in reality, a mosaic of point sources of light. Some of these points are very bright, some are very weak, and they vary in color. Each point source of light on the object comes to a separate point focus on the opposite side of the lens in line with the lens center. If a white sheet of paper is placed at the focus distance from the lens, one can see an image of the object, as demonstrated in Figure 49-7B. However, this image is upside down with respect to the original object, and the two lateral sides of the image are reversed. This is the method by which the lens of a camera focuses images on film.

Measurement of the Refractive Power of a Lens—"Diopter"

The more a lens bends light rays, the greater is its "refractive power." This refractive power is measured in terms of diopters. The refractive power in diopters of a convex lens is equal to 1 meter divided by its focal length. Thus, a spherical lens that converges parallel light rays to a focal point 1 meter beyond the lens has a refractive power of +1 diopter, as shown in Figure 49-8. If the lens is capable of bending parallel light rays twice as much as a lens with a power of +1 diopter, it is said to have a strength of +2 diopters, and the light rays come to a focal point 0.5 meter beyond the lens. A lens capable of converging parallel light rays to a focal point only 10 centimeters (0.10 meter) beyond the lens has a refractive power of +10 diopters.

The refractive power of concave lenses cannot be stated in terms of the focal distance beyond the lens because the light rays diverge, rather than focus to a point. However, if a concave lens diverges light rays at the same rate that a 1-diopter convex lens converges them, the concave lens is said to have a dioptric strength of -1. Likewise, if the concave lens diverges light rays as much as a +10-diopter lens converges them, this lens is said to have a strength of -10 diopters.

Concave lenses "neutralize" the refractive power of convex lenses. Thus, placing a 1-diopter concave lens immediately in front of a 1-diopter convex lens results in a lens system with zero refractive power.

The strengths of cylindrical lenses are computed in the same manner as the strengths of spherical lenses, except that the axis of the cylindrical lens must be stated in addition to its strength. If a cylindrical lens focuses

Effect of lens strength on the focal distance.

parallel light rays to a line focus 1 meter beyond the lens, it has a strength of +1 diopter. Conversely, if a cylindrical lens of a concave type diverges light rays as much as a +1-diopter cylindrical lens converges them, it has a strength of -1 diopter. If the focused line is horizontal, its axis is said to be 0 degrees. If it is vertical, its axis is 90 degrees.

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