A contact lens prescription calls for +2.25-diopter lenses...

A contact lens prescription calls for $+2.25$-diopter lenses with inner curvature radius $8.6 \mathrm{~mm}$ to fit the patient's cornea. (a) If the lenses are plastic with $n=1.56$, what should be the outer curvature radius? (b) With these lenses, the patient comfortably reads a newspaper $30 \mathrm{~cm}$ from her eyes. Where's the image as viewed through the lenses?

Key Concepts

Thin Lens Equation

The thin lens equation connects the object distance, the image distance, and the focal length of a lens. This equation is used to determine where an image will form when light passes through a lens, which is fundamental in understanding how lenses, including contact lenses, modify the perceived location of objects.

Curved Surface Geometry

In lens design, the geometry of the curved surfaces, including inner and outer curvature radii, significantly impacts the lens’s optical performance. Understanding how the shape of a lens surface influences the path of light is crucial in designing lenses that fit specific prescriptions, such as those used in contact lenses.

Lensmaker's Equation

This equation relates the refractive index, the radii of curvature of the lens surfaces, and the lens’s effective focal length or power. It is essential in determining how changing the curvature of one surface affects the overall optical properties of a lens, which is particularly important in lens design such as in contact lenses.

Diopters and Focal Length

Diopters are a measure of the optical power of a lens, defined as the inverse of the focal length in meters. This concept bridges the relationship between a prescribed correction in diopters and the physical configuration of the lens, allowing one to design a lens that meets the required optical power.

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