Final answer:
The power of the woman's eyes is 12.5 D. The image size of a 1.00-mm object held at a distance of 8.00 cm is -0.08 mm. The image size would be -0.25 mm if the object were held at the normal distance.
Step-by-step explanation:
The power of the eyes can be determined using the equation P = 1/f, where P is the power in diopters and f is the focal length in meters. We can convert the distance from centimeters to meters by dividing by 100. Therefore, the power for the woman who can see an object clearly at a distance of 8.00 cm is 1/(0.08) = 12.5 D.
The image size can be determined using the magnification formula, M = -di/do, where M is the magnification, di is the image distance, and do is the object distance. The magnification is the ratio of the image size to the object size. In this case, the object size is 1.00 mm. Substituting the values into the formula, we can solve for di:
M = di/do
-1 = di/(0.08)
di = -0.08 mm
Therefore, the image size of the 1.00-mm object held at a distance of 8.00 cm is -0.08 mm.
If the object is held at the normal distance of 25.0 cm, we can use the same formula to determine the image size:
M = di/do
-1 = di/(0.25)
di = -0.25 mm
Therefore, the image size would be -0.25 mm if the object were held at the normal distance.