A person has a near point at 100 cm . What power of lens is...

The person wants to read at a distance of $20 \text{ cm}$. Therefore, the object distance is $u = -20 \text{ cm} = -0.2 \text{ m}$.

The near point of the person is $100 \text{ cm}$. The lens must form the image of the object at this near point. Therefore, the image distance is $v = -100 \text{ cm} = -1 \text{ m}$.

Using the lens formula, the power $P$ of the lens is given by:

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

Substituting the values of $v$ and $u$:

$P = \dfrac{1}{-1} - \dfrac{1}{-0.2}$

$P = -1 + 5 = +4 \text{ D}$