A person sees clearly when he wears eyeglasses that have a...

A person sees clearly when he wears eyeglasses that have a power of $-4.00$ diopters and sit 2.00 $\mathrm{cm}$ in front of his eyes. If the person wants to switch to contact lenses, which are placed directly on the eyes, what lens power should be prescribed?

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Key Concepts

Diopter

A diopter is the standard unit for measuring the optical power of a lens. It is defined as the reciprocal of the focal length (in meters) and indicates the ability of the lens to converge or diverge light. A negative diopter value, as seen in the problem, indicates a diverging lens used to correct myopia.

Vertex Distance

Vertex distance refers to the physical distance between the back surface of a corrective lens (such as glasses) and the cornea of the eye. This distance is crucial because it affects the effective power experienced by the eye. Changes in vertex distance—like moving from glasses to contact lenses—can lead to a difference in the refractive power needed to achieve the same visual correction.

Effective Power Adjustment

Effective power adjustment is the process of recalculating the necessary lens power when the position of the corrective lens relative to the eye is altered. In the context of switching from eyeglasses (which sit at a finite vertex distance) to contact lenses (which rest directly on the eye), the prescription must be adjusted to account for the elimination of the vertex distance, ensuring that the corrected image is properly focused on the retina.

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