To correct Darcy's farsightedness with contact lenses, we must calculate the lens power needed to adjust the eye's focus onto the retina at the lens-to-retina distance. Given Darcy's most accommodated state focal length of 19.8 mm, the required contact lens power would be the difference between 50.0 D and Darcy's natural eye power at its closest focus.
To determine the strength of contact lenses needed to correct farsightedness in Darcy's eyes, we can use the lens formula which relates the focal length of the lens (f) to its power (P), given by P = 1/f, with P in diopters (D) when f is in meters. Darcy's focal length is given as 19.8 mm for the most accommodated state, which is 0.0198 meters. Since the eye's power ranges from 50.0 D to 54.0 D for distant to close vision, and the lens of the eye has an 8% accommodation ability, we need to ensure the added lens power brings Darcy's maximum eye power to an appropriate level to focus images on the retina, which is at the 20.0 mm (or 2.00 cm) lens-to-retina distance.
The natural power for close vision is 54.0 D, but because this is in Darcy's most accommodated state, the eyes are not focusing properly. We, therefore, need to calculate the difference in power required to allow clear vision at the standard lens-to-retina distance. The power needed is thus 1/(2.00 cm) - natural eye power, which is approximately 1/0.020 m - 54.0 D = 50.0 D. So the power of the lens required to correct Darcy's farsightedness would be 50.0 D - natural accommodated eye power. Assuming no additional complications, this should correct the farsightedness when the lenses are placed directly on the eyes.
The complete question is- Darcy suffers from farsightedness equally severely in both eyes. The focal length of either of Darcy's eyes is 19.8 mm in its most accommodated state (i.e, when the eye is focusing on the closest object that it can clearly see) What lens strength (a.k.a., lens power) of contact lenses should be prescribed to correct the farsightedness in Darcy's eyes? (Assume the lens-to retina distance of Darcy's eyes is 2.00 cm, and the contact lenses are placed a negligibly small distance from the front of Darcy's eyes)