There are multiple synonyms for the phrase "his eye spanned the intervening space." One such synonym could be "he surveyed the distance with his gaze." Another option could be "his vision scanned the expanse in front of him." A similar phrase could be "he looked across the intervening space." Additionally, "he gazed over the gap before him" could be used. All of these phrases convey the idea of someone using their senses to comprehend the area in front of them. Depending on the context, different synonyms may be more appropriate to use. Overall, there are many ways to express the concept of someone observing the distance between two points.