The power of a lens is given by:
\[
P = \frac{100}{f}
\]
where:
- \( P \) is the power in diopters (D),
- \( f \) is the focal length in centimeters.
For \( P = 2D \):
\[
f = \frac{100}{2} = 50 \text{ cm}
\]
The near point of a person using glasses is the focal length of the corrective lens.
Thus, the correct answer is \(\boxed{50 \text{ cm}}\).