Traditionally, most of the terminology of geometrical optics was developed with reference to spherical reflecting and refracting surfaces. Aspherical surfaces, however, are sometimes involved. The optic axis is a reference line that is an axis of symmetry. If the optical component is spherical, the optic axis passes through the center of a lens or mirror and through the center of curvature. Light rays from a very distant source are considered to travel parallel to one another. If rays parallel to the optic axis are incident on a spherical surface, they are reflected or refracted so that they intersect or appear to intersect at a point on the optic axis. The distance between this point and the vertex of a mirror or a thin lens is the focal length. If a lens is thick, calculations are made with reference to planes called principal planes, rather than to the surface of the lens. A lens may have two focal lengths, depending on which surface (if the surfaces are not alike) the light strikes first. If an object is at the focal point, the rays emerging from it are made parallel to the optic axis after reflection or refraction. If rays from an object are converged by a lens or mirror so that they actually intersect in front of a mirror or behind a lens, the image is real and inverted, or upside down. If the rays diverge after reflection or refraction so that the light only appears to converge, the image is virtual and erect. The ratio of the height of the image to the height of the object is the lateral magnification.
If it is understood that distances measured from the surface of a lens or mirror in the direction in which light is traveling are positive and distances measured in the opposite direction are negative, then if u is the object distance, v the image distance, and f is the focal length of a mirror or of a thin lens, the equation
applies to spherical mirrors, and the equation
applies to spherical lenses. If a simple lens has surfaces with radii r1 and r2, and the ratio of its refractive index to that of the medium surrounding it is n, then
The focal length of a spherical mirror is equal to half the radius of curvature. As is shown in Fig. 7, rays parallel to the optic axis that are incident on a concave mirror with its center of curvature at C are reflected so that they intersect at B, halfway between A and C. If the object distance is greater than the distance AC, then the image is real, inverted, and diminished. If the object lies between the center of curvature and the focal point, the image is real, inverted, and enlarged. If the object is located between the surface of the mirror and the focus, the image is virtual, upright, and enlarged. Convex mirrors form only virtual, erect, and diminished images.
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