Final answer:
To find the refractive power for the contact lenses for the farsighted librarian, one must consider the minimum reading distance with eyeglasses (her near point) and calculate the inverse of this distance. As contact lenses sit directly on the eyes, their required refractive power would be approximately 3.44 diopters.
Step-by-step explanation:
The question involves the calculation of the refractive power of contact lenses for a farsighted librarian. The librarian's current eyeglasses have a refractive power of 3.84 D and are worn 0.025 m away from the eyes, with a minimum reading distance of 0.2911 m. In order to find the refractive power for the contact lenses, we can use the formula for lens power (P) given by P = 1/f, where f is the focal length of the lens in meters.
The librarian's ability to read at a minimum distance of 0.2911 m without contact lenses implies that this distance is her near point (the closest distance at which she can see clearly). When wearing glasses, this near point is effectively adjusted by the eyeglasses' power. The total effective focal length (F') can be found using the formula F' = f - d, where d is the distance from the eyeglasses to the eyes. However, since contact lenses are worn directly on the cornea, the distance d is considered to be zero, removing the need to adjust the focal length as with eyeglasses.
For contact lenses, the focal length of the lens must match the near point of the eye, so the required refractive power for the contact lenses (Pc) is simply the inverse of the near point (Np), or Pc = 1/Np.
By using this information, we can find the required refractive power for the contact lenses:
Pc = 1/0.2911 m
Pc = 3.436 D
The refractive power for the contact lenses should be approximately 3.44 diopters.