What is Reduced eye? — Physics

Definition 4.1 University Physics — Year 1 · Chapter 4 — Optical Instruments and the Eye

The reduced eye models the cornea and the crystalline lens as a single thin converging lens of variable focal length, and the retina as a screen at a fixed distance $d \approx 17\,\mathrm{mm}$ behind it. Muscles change the lens’s curvature to keep the image of the object looked at on the retina: this is accommodation. The iris in front of the lens is a variable aperture of diameter $2\,$ to $8\,\mathrm{mm}$ , the pupil.

Examples

Example 4.3 (The eye’s vergence)

Distant object: image at $d = 17\,\mathrm{mm}$ means $f' = 17\,\mathrm{mm}$ , $V = 1/0.017 = 59\,\delta$ . Object at $25\,\mathrm{cm}$ : $V = 1/0.017 + 1/0.25 = 59 + 4 = 63\,\delta$ . Four diopters of accommodation out of sixty: the crystalline lens adds only a few percent to the cornea’s job, but those few percent are everything for reading.

Example 4.9 (A watchmaker’s loupe)

$f' = 25\,\mathrm{mm}$ : $G = 250/25 = 10$ , sold as “ $10\times$ ”. A $0.05\,\mathrm{mm}$ detail then subtends $2 \times 10^{-3}\,\mathrm{rad}$ , comfortably resolved. Pushing $G$ higher means $f'$ of a few millimeters, a tiny lens held against the eye — the limit of the single lens, and the reason the microscope exists.

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Examples

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