Optical systems are frequently employed to obtain images of a more convenient size for study than the original objects. Magnifiers and microscopes provide enlarged images of inconveniently small objects; telescopes and binoculars provide smaller, more conveniently located images of immense objects that are very far away. The relocation of images is described by the vergence equation. Magnification is also readily determined in this context. For objects of finite size and distance, transverse magnification—the ratio of the height (or distance from the optic axis) of an image to the height of the original source object—is the most appropriate description. Transverse magnification (sometimes referred to as “lateral magnification” or “linear magnification”) is denoted by MT. For lenses in air, a simple calculation with similar triangles (Figure 1-17) gives MT = h2/h1 = ν/u. Here, u and ν carry the same sign conventions as used in the vergence equation. (If the lens separates media of refractive indices n1 and n2, the corresponding formula is MT = n1ν/n2u. The refractive index for the object medium multiplies the image distance and vice versa!) Negative values of MT indicate images that are upside-down (inverted), not images that are reduced in size (“minified”), which correspond to values of MT less than 1 in absolute value.
Figure 1-17 Ray tracing for a convex lens used as a magnifier in air. Notice how the principal ray through the central point of the lens creates similar triangles, indicating that the transverse magnification is proportional to the ratio of image distance to object distance.
(Illustration developed by Scott E. Brodie, MD, PhD.)
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.