Final answer:
The focal length of contact lenses needed for a nearsighted person with a 130 cm far point to focus on the stars is 130 cm, which corresponds to a lens power of 0.769 diopters, expressed to three significant figures.
Step-by-step explanation:
To find the focal length of contact lenses that would allow a nearsighted person with a 130 cm far point to focus on the stars, we use the lens formula 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance, and u is the object distance. Since we want the person to focus on the stars, we consider the stars at an infinite distance; hence v = ∞ and 1/v = 0. The object distance u is the nearsighted person's far point which is 130 cm, but it should be taken as negative in the lens formula as per convention, so u = -130 cm.
Plugging these values into the lens formula:
1/f = 1/∞ - 1/(-130 cm) = 0 - (-1/130 cm) = 1/130 cm. Therefore, f = 130 cm.
The power P of the lens is given by P = 1/f (in meters), so to convert the focal length from centimeters to meters, we divide by 100: P = 1/(130 cm / 100) = 1/1.3 m = 0.769 D, and to three significant figures, this is P = 0.769 D.