Final answer:
The appropriate contact lens power for a farsighted person to see clearly at a distance of 25 cm when their near point is 80 cm would be calculated using the lens formula and results in a value of +4.00 D. Since this is not one of the available options, the nearest is +3.00 D.
Step-by-step explanation:
When considering the correction of vision for a farsighted person, it is essential to understand the concept of diopters. Diopters (D) measure the optical power of a lens, with positive diopters being used for farsightedness and negative for nearsightedness. In this case, we are looking at a farsighted person whose near point is 80 cm. To correct this individual's vision to see clearly at a standard reading distance (25 cm), we require a lens that can adjust the near point from 80 cm to 25 cm.
To calculate the necessary lens power, we use the lens formula: 1/f = 1/d_o + 1/d_i, where f is the focal length of the lens, d_o is the object distance, and d_i is the image distance. Here, d_o would become 25 cm (converted to meters, since diopters is a metric unit), and we aim to adjust the near point from 80 cm to 25 cm.
Since the person can see things clearly when they are 80 cm away, their eyes can form an image at infinity without assistance. This means that for their near point to be 25 cm, the lens needs to have a focal length that takes an object at 25 cm and forms an image at infinity. To find the focal length (f), we can set the corrected near point (d_o = -25 cm, using a negative sign since the object is on the same side as the light is coming from) and solve for f using the lens equation.
The optical power (P) of the lens is then calculated as P = 1/f. Plugging in our values, we get P = 1/(-25 cm) = -4 D. However, because the person is farsighted, we require positive diopters, which means we are looking for a positive version of the calculated power. Hence, the prescription would need to be +4.00 D. Among the given options, we do not have +4.00 D, so if we round it to the nearest available option, it would be +3.00 D (option c).