The person's far point is 400 cm, which means they cannot see clearly beyond this distance. This condition is known as Myopia or Nearsightedness.

1. Type of Lens: To correct myopia, a concave lens is used to diverge incoming parallel rays from infinity so that they appear to diverge from the person's actual far point.
2. Calculation: Object distance ($u$) = $\infty$ (since we want to see objects at infinity). Image distance ($v$) = Distance of the person's far point = $-400$ cm (virtual image formed in front of the eye). Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ $\frac{1}{f} = \frac{1}{-400} - \frac{1}{-\infty} = -\frac{1}{400}$ Focal length ($f$) = $-400$ cm = $-4$ m. Power ($P$) = $\frac{1}{f \text{ (in meters)}} = \frac{1}{-4} = -0.25$ Diopter (D).

Thus, the required lens is concave with a power of $-0.25$ D.