For a linear array with aperture D, the near-field distance N increases with D^2; which of the following statements is true?

• A. N decreases with increasing D
• B. N is independent of D
• C. N increases with D
• D. N increases with D^2

Answer: (D)

The key idea is how the boundary between near field (Fresnel region) and far field for a finite aperture scales with aperture size. For a linear array of width D, the distance at which the wavefront becomes effectively planar and the beam pattern stabilizes grows with D in a specific way: the far-field boundary is on the order of D^2 divided by the wavelength, so the near-field distance scales as N ∝ D^2 (for a fixed wavelength). This means that increasing the aperture makes the near field extend farther out, and doubling the aperture makes N increase by a factor of four, while tripling it makes N nine times larger. The squared dependence reflects the geometric and phase considerations across the aperture that determine when the wavefront transitions to the far field. Therefore, the statement that N increases with D^2 is the correct one. The other possibilities contradict this scaling: N does not stay constant, it does not rise only linearly with D, and it does not decrease with increasing D.