Final answer:
The strength of a human eye for distant vision is 50.0 diopters (D). A young woman with a 10% accommodation ability can see objects clearly that are as close as 22.7 cm. For a woman to see an object at 8 cm, her eye would need a power of 12.5 D.
Step-by-step explanation:
The strength of a human eye while viewing a distant object is essentially the eye's ability to focus light to form a clear image on the retina. This strength, quantified as optical power, is measured in diopters (D). The normal power for distant vision is 50.0 D, and for a typical eye with a 2.00 cm lens-to-retina distance, the power ranges from this value up to 54.0 D when the eye is fully accommodated for close vision. A 10.0% accommodation ability means that the eye can increase its power by 10% for close vision. Therefore, a young woman with normal vision and a 10.0% ability to accommodate can see objects clearly that are as close as approximately 22.7 cm away (calculated by taking the inverse of the total accommodative power, which is 50.0 D + 10.0% of 50.0 D).
When considering the power of the eyes of a woman who can see an object clearly at only 8.00 cm, her eyes must have a much higher power to focus light from such a short distance onto her retina. The power required would be the inverse of the distance in meters to the object, which translates to 1/0.08 m = 12.5 D. This is significantly higher than the normal power for distant vision, indicating a high degree of accommodation.
The process known as accommodation involves adjusting the focal length and power of the lens within the eye to maintain a sharp image on the retina for objects at various distances. It is interesting to note that the image must fall precisely on the retina to produce clear vision, regardless of the object's distance. As we age, our ability to accommodate diminishes, a condition known as presbyopia, requiring the use of reading glasses for close tasks.