Final answer:
The power of the corrective lens needed to correct the nearsightedness of an individual with a far point of 54.0 cm is -1.85 diopters.
Step-by-step explanation:
To correct the nearsightedness of an individual with a near point of 15.0 cm and a far point of 54.0 cm, we need to determine the power of the corrective lens. Nearsightedness means that the eye can only see objects clearly when they are relatively close. The farthest point at which a nearsighted person can see clearly is known as the far point.
The formula to find the power P of a lens in diopters is P = 1/f, where f is the focal length in meters. The focal length for corrective lenses would be the distance from the lens to the far point when adjusted to the standard viewing distance (infinity). However, if the lens is supposed to bring objects at infinity into focus at the person's far point, the focal length of the lens would be the negative of the far point distance, in meters, because the lens must diverge light rays.
The power of the corrective lens needed for this person's far point of 54.0 cm (0.54 meters) is P = -1/0.54 meters = -1.85 diopters. This means the individual requires a lens with a power of -1.85 diopters to correct their vision for distance.