Final answer:
The retired bank president needs eyeglass lenses with a focal length of 41.2 cm or a power of approximately 2.4 diopters to read at a distance of 25.2 cm comfortably.
Step-by-step explanation:
The question is about determining the focal length of eyeglass lenses needed by a retired bank president so that she can read at a comfortable distance of 25.2 cm, given that she can currently only read fine print at a distance of no closer than 62.0 cm.
Step-by-Step Solution:
To find the necessary focal length of the eyeglass lens, we need to apply the lens formula: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens.
Since the desired reading distance is 25.2 cm (do), and the glasses create an image at the person's near point distance of 62.0 cm (di), we plug these values into the lens formula.
Our formula is now 1/f = 1/25.2 + 1/(-62.0), because the image would be virtual and located on the same side of the lens as the object (hence the negative sign).
Solving for f, we find that f = 41.2 cm. However, this value must be converted into diopters (D), the unit commonly used for the power of a lens, which is the reciprocal of the focal length in meters. Therefore, the power P is P = 1/f(meters).
After converting cm to meters, the calculation for power in diopters will be P = 1/0.412 ≈ 2.4D.
Thus, the retired bank president would need eyeglass lenses with a focal length of 41.2 cm or a power of approximately 2.4 diopters.