Final answer:
Ben Ryan needs eyeglasses with a power of -8 diopters to correct his nearsightedness, allowing his far point to be at infinity.
Step-by-step explanation:
Determining the Lens Power for Ben Ryan's Glasses
Ben Ryan is nearsighted with a far point at 50 cm from his eye. We're assuming his eyeglasses are worn 10 cm in front of his eyes. The lens formula we use is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Since the far point is the maximum distance at which he can see objects clearly, we can set do at 50 cm (0.5 m). The image distance di will be the distance from the glasses to the nearsighted eye's far point, which is -10 cm (-0.1 m) because it is virtual. The negative sign indicates that the image is formed on the same side of the lens as the object.
Plugging the values into the lens formula, we get 1/f = 1/0.5m + 1/(-0.1m) = 2 D - 10 D = -8 D. The negative diopter value indicates a diverging lens, which is suitable for correcting myopia.
Therefore, the power of the lenses that Ben Ryan needs for his glasses is -8 diopters.