The power of a lens is a measure of its ability to refract light. It is measured in diopters (D). In the context of this question, a lens is used to correct for a short-sighted eye, which means that the eye can see objects up close clearly, but has difficulty seeing distant objects.

The far point is the maximum distance at which the eye can focus. In this case, the far point of the short-sighted eye is given as 200 cm. To calculate the power of the lens, we need to use the formula:

Power (in Diopters) = 1 / Focal Length (in meters)

The focal length is the distance at which a lens brings parallel rays of light to a focus. In this case, since the eye is short-sighted, the lens is used to diverge the light and allow it to focus properly on the retina.

Since the far point is given in centimeters, we need to convert it to meters by dividing it by 100. Therefore, the focal length would be 200 cm / 100 = 2 meters.

Plugging this value into the formula, we get:

Power = 1 / 2 = 0.5D

Therefore, the correct answer is option