What is the radius of curvature for a lens with a power of 4.00D?

To find the radius of curvature of a lens given its power, you can use the formula relating power (P) to focal length (f) and the lensmaker's equation. The power of a lens is defined as the inverse of its focal length in meters:

[ P = \frac{1}{f} ]

Given that the power is 4.00 diopters, we can calculate the focal length:

[ f = \frac{1}{P} = \frac{1}{4.00} = 0.25 \text{ m} ]

Next, we can relate the focal length to the radius of curvature (R) of the lens. For a thin lens in air, the lensmaker's formula can be simplified for a lens of a given refractive index (n) to show this relationship. For a biconvex lens, which typically has a positive power, the focal length can be approximated by:

[ f = \frac{R}{2(n-1)} ]

If we assume the lens is made from a standard material, such as crown glass (with ( n \approx 1.5 )), we can rearrange the formula to solve for R:

Given that:

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