A nearsighted person cannot clearly see past 200 cm . Determine the...

For a nearsighted (myopic) eye, the lens must form an image of an object at infinity at the far point of the eye.

Given the far point is $200 \text{ cm}$, the image distance is $v = -200 \text{ cm} = -2 \text{ m}$.

The object distance is $u = -\infty$.

Using the lens formula:

$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

$\dfrac{1}{f} = \dfrac{1}{-2} - \dfrac{1}{-\infty}$

$\dfrac{1}{f} = -0.5 \text{ m}^{-1}$

The power of the lens is $P = \dfrac{1}{f} = -0.5 \text{ D}$.