A person sees clearly wearing eyeglasses that have a power of −2.92 diopters and sit 2.22 cm in front of the eyes.
If the person wants to switch to contact
lenses, which are placed directly on the eyes,what lens power should be prescribed?
Answer in units of diopter.
To determine the lens power that should be prescribed for contact lenses, we need to understand the relationship between the power of eyeglasses and contact lenses.
The lens power of eyeglasses represents the amount of refractive correction needed for clear vision. It is usually measured in diopters (D). A negative power indicates nearsightedness (myopia).
When eyeglasses are worn, they are placed at a certain distance in front of the eyes. This distance is called the vertex distance. In this case, the glasses sit 2.22 cm in front of the eyes. This vertex distance affects the effective power of the eyeglasses.
To switch to contact lenses, we need to find the equivalent lens power that would provide the same refractive correction as the glasses, but with the lenses placed directly on the eyes (zero vertex distance).
To calculate the equivalent lens power, we can use the following formula:
Equivalent Power = Glasses Power - (Glasses Power * (Vertex Distance / 100))
Let's apply this formula to the given values:
Glasses Power = -2.92 diopters
Vertex Distance = 2.22 cm = 0.022 meters
Equivalent Power = -2.92 - (-2.92 * (0.022 / 100))
Equivalent Power = -2.92 - (-0.0006424)
Equivalent Power ≈ -2.919
Therefore, the lens power that should be prescribed for the contact lenses is approximately -2.919 diopters.