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  • 2020–2021 BCSC Basic and Clinical Science Course™

    Go to Academy Store Learn more and Purchase.

    3 Clinical Optics

    Chapter 1: Geometric Optics

    General Refracting Systems

    Axial (Longitudinal) Magnification

    As we have seen, a thin lens in air produces a transverse magnification described by the simple equation MT = ν/u. If the source “object” is in fact an assemblage of objects, or an extended object with a palpable axial dimension (measured along the optic axis), the image will also exhibit an axial extent, or apparent thickness. We can show (for example, by differentiating the vergence equation) that the apparent thickness of the image—the axial, or longitudinal, magnification for a refracting system in air—is given by

    M L = (MT)2

    Figure 1-18 illustrates this relationship.

    This effect leads to a substantial distortion of the images seen by direct or indirect ophthalmoscopy. Although it is difficult to appreciate image depth with the monocular view through the direct ophthalmoscope, the aerial image seen with the indirect ophthalmoscope is generally seen stereoscopically. Depending on the power of the condensing lens used, the distortion factor may vary as much as fourfold in changing from a 14-D lens to a 30-D lens. The overall stereoscopic effect is reduced by the small interpupillary distance of the periscopic viewing system but, nevertheless, the perceived shape of fundus features, such as tumors or optic disc excavation, is typically somewhat exaggerated.

    Figure 1-18 Ray tracing for a convex lens in air. The source object is the red circle; its image is the ellipse. Notice the considerable distortion caused by the disparity between transverse and axial magnifications.

    (Illustration developed by Scott E. Brodie, MD, PhD.)

    EXAMPLE 1-8

    Compute the relative apparent thickness of the retinal features as seen by indirect ophthalmoscopy with a 15-D, 20-D, and 30-D condensing lens. (Assume a total power for the eye of 60 D.)

    The transverse magnification of an indirect ophthalmoscope is equal to the ratio of the power of the eye (about 60 D) to the power of the condensing lens (similar to the formula for the power of a Keplerian telescope). The axial magnification is given by ML = (MT)2. Although the apparent thickness (or depth) of retinal features is reduced by the periscopes built into the indirect ophthalmoscope (which reduce the effective interocular distance of the examiner) compared with normal viewing, the relative depth of fundus features is unaffected. The ratio of the transverse magnification provided by 15 D, 20 D, and 30 D condensing lenses is then 4×, 3×, and 2×, respectively, so the relative axial magnifications are in the ratios of 16:9:4, respectively. Thus, the apparent retinal thickness as seen with a 15 D condensing lens is nearly double that seen with the 20 D lens, and 4 times that seen with the 30 D lens.

    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.

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