Final answer:
A neutron star is detected from Earth as a pulsar when its narrowly focused radiation beam, similar to a lighthouse's beam sweeping across the sea, intersects with Earth's position in space.
Step-by-step explanation:
A neutron star is detected from Earth as a pulsar by its regular radio pulses only if Earth lies within the narrow beam of radiation emitted by the neutron star's magnetic poles. This phenomenon is similar to a lighthouse that sweeps its beam across the ocean; ships see the light only when the beam points toward them. In space, the pulsar's beam sweeps across in a circle, but because space is three-dimensional, there's no guarantee that Earth will be within this circle. Consequently, many pulsars exist whose beams do not intersect with Earth, making them undetectable to us. The alignment of the neutron star's magnetic poles and its rotational axis is crucial; if they are misaligned, the rotation will carry the poles into and out of our line of sight, causing us to see a pulse of radiation as each pole points towards Earth.