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Magnification in Ophthalmic Optics

Optics & Refraction

Teaching images

Exam pearl

Imagine standing in front of a funhouse mirror. The image of your face looks either enormous or tiny - not because your face changed, but because the mirror altered the angular subtense of the image at your eye. This, at its core, is what every optical magnifying system does: it manipulates the angle subtended by the image at the observer's eye relative to the angle subtended by the object at the naked eye (or at a reference distance). Every loupes, slit-lamp, indirect ophthalmoscope, and fundus camera you will use in your career is, mathematically, just a controlled funhouse mirror.

Types of Magnification - Master Table

Types of Magnification - Master Table
Type	Definition	Formula	Key Instruments	Nature of Image
Transverse (Linear)	• Ratio of image height to object height	• m = −v/u = I/O • Negative = inverted	• Camera • Reduced eye model	• Real / inverted • Virtual / erect
Angular (Magnifying Power)	• Ratio of angle subtended by image (with aid) to angle subtended by object at 25 cm (D)	• M = D/f = 25/f (cm) for simple lens with final image at infinity • M = 1 + D/f when final image is at the near point	• Loupe • Simple magnifier	• Virtual • Erect
Longitudinal (Axial)	• Magnification along the optical axis	• Longitudinal magnification = (transverse magnification)² in the air/paraxial approximation • Longitudinal magnification = (transverse magnification)²/n when refractive-index effects are included	• Important in optical coherence tomography (OCT) depth scaling • Axial optical distances are converted to geometrical distances using the medium’s refractive index	• Real or virtual
Relative Size Magnification	• Making the object physically larger (e.g., large-print books)	• M = new object size / original object size	• Large-print materials	• Not applicable
Relative Distance Magnification	• Bringing the object closer to the eye	• M = D_original / D_new • e.g., 40 cm → 10 cm = 4×	• Low-vision rehabilitation	• Not applicable
Projection Magnification	• Projecting enlarged image on a screen	• M = −image distance / object distance	• Slide projectors	• Real, inverted

Types of Magnification - Master Table
Type	Definition	Formula	Key Instruments	Nature of Image
Transverse (Linear)	• Ratio of image height to object height	• m = −v/u = I/O • Negative = inverted	• Camera • Reduced eye model	• Real / inverted • Virtual / erect
Angular (Magnifying Power)	• Ratio of angle subtended by image (with aid) to angle subtended by object at 25 cm (D)	• M = D/f = 25/f (cm) for simple lens with final image at infinity • M = 1 + D/f when final image is at the near point	• Loupe • Simple magnifier	• Virtual • Erect
Longitudinal (Axial)	• Magnification along the optical axis	• Longitudinal magnification = (transverse magnification)² in the air/paraxial approximation • Longitudinal magnification = (transverse magnification)²/n when refractive-index effects are included	• Important in optical coherence tomography (OCT) depth scaling • Axial optical distances are converted to geometrical distances using the medium’s refractive index	• Real or virtual
Relative Size Magnification	• Making the object physically larger (e.g., large-print books)	• M = new object size / original object size	• Large-print materials	• Not applicable
Relative Distance Magnification	• Bringing the object closer to the eye	• M = D_original / D_new • e.g., 40 cm → 10 cm = 4×	• Low-vision rehabilitation	• Not applicable
Projection Magnification	• Projecting enlarged image on a screen	• M = −image distance / object distance	• Slide projectors	• Real, inverted

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