A woman can read the large print in a newspaper only when it...

A woman can read the large print in a newspaper only when it is at a distance of $65 \mathrm{cm}$ or more from her eyes. (a) Is she nearsighted (myopic) or farsighted (hyperopic), and what kind of lens is used in her glasses to correct her eyesight? (b) What should be the refractive power (in diopters) of her glasses (worn $2.0 \mathrm{cm}$ from the eyes), so she can read the newspaper at a distance of $25 \mathrm{cm}$ from her eyes?

Key Concepts

Hyperopia (Farsightedness)

Hyperopia is a common refractive error where the near point of clear vision is abnormally far from the eyes. In individuals with hyperopia, objects at close range appear blurred because the eye’s lens has insufficient converging power to focus the image sharply on the retina. Correcting hyperopia involves shifting the near point closer to a normal reading distance.

Converging (Convex) Lenses for Vision Correction

To correct hyperopia, converging (convex) lenses are used. These lenses add positive refractive power, effectively converging incoming light rays so that the image of a near object is formed further back, ideally on the retina. This optical adjustment assists the eye in focusing on objects at closer distances than its unaided near point.

Lens Formula and Sign Conventions

The thin lens formula (1/f = 1/v + 1/u) is fundamental in calculating the necessary focal length of corrective lenses. Correct application of the sign convention (where object distances are taken as positive and virtual image distances as negative for a lens producing a virtual image) allows for determination of the lens power required to shift the effective image position from an object at a desired distance to the patient’s unaided near point.

Refractive Power and Diopters

Refractive power, measured in diopters, is defined as the inverse of the focal length in meters (P = 1/f). In prescribing corrective lenses for hyperopia, calculating the appropriate diopter value is essential to ensure that the lens provides enough converging power to move the near point to a normal reading distance. This process involves converting focal length from centimeters to meters and taking its reciprocal.

Vertex Distance Correction

Vertex distance refers to the separation between the corrective lens and the eye. When glasses are not in direct contact with the eye, this gap must be considered as it slightly alters the effective object and image distances used in the lens formula. Adjusting for vertex distance is important for accurately calculating the refractive power of the lens needed for proper vision correction.

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