Final answer:
To determine the closest object a person with normal distant vision can see clearly, we need to calculate the power of their eyes when fully accommodated. Using the lens formula and the fully accommodated power, we find that the closest object they can see clearly is approximately 18.18 cm away from their eye.
Step-by-step explanation:
To determine the closest object a person with normal distant vision can see clearly, we need to calculate the power of their eyes when fully accommodated. Since they have a 10.0% ability to accommodate, we can increase their normal power of 50.0 D by 10%. This results in a power of 55.0 D.
In optics, the lens formula, 1/f = 1/v - 1/u, relates the object distance (u), image distance (v), and focal length (f) of a thin lens. For a person with normal distant vision, their furthest point of clear vision is at infinity, which means the image distance (v) is also at infinity, and the formula simplifies to 1/f = 0. Therefore, we can assume the person with normal distant vision has a focal length (f) of 0.
Using the lens formula with the fully accommodated power of 55.0 D and the focal length of 0, we can calculate the object distance (u) by rearranging the formula to u = 1/f + 1/v. Solving for v, we find that v = 1/u - 1/f = -1/55 - 1/0 = -1/55 D.
Since the object distance (u) is negative, it means the object is closer to the eye than the focal point. The absolute value of the object distance gives us the distance from the eye to the closest object the person can see clearly. Therefore, the closest object they can see clearly is approximately 18.18 cm away from their eye.