Wh at is the power of the lens, if the far point of a short-sighted eye is 200 cm?

A short-sighted (myopic) eye cannot see objects clearly beyond its far point. To correct this, a diverging (concave) lens is used to form a virtual image of a distant object (at infinity) at the person's far point [t1][t2]. According to the lens formula (1/f = 1/v - 1/u), where the object distance (u) is infinity and the image distance (v) is the far point, the focal length (f) of the corrective lens is equal to the negative of the far point distance [t2][t5]. In this case, the far point is 200 cm, which equals 2 meters. Therefore, f = -2 m. The power of a lens (P) is the reciprocal of its focal length in meters (P = 1/f) [t2][t8]. Calculating the power gives P = 1/(-2) = -0.5 Dioptres (D) [t3]. The negative sign indicates a concave lens, which is standard for myopia correction [t5].

Sources

1. [1] https://en.wikipedia.org/wiki/Far_point