You will quickly notice that sometimes the video connection only works at close distance, while at other times the range seems much better. This depends on whether the other device can be contacted on the currently used Wi-Fi network. If it can't, the airdrop-like connection is established, which only works for up to about 5..10 m (15..30 ft). This alrady gives us huge improvement in eye separation, but what if there is no Wi-Fi nearby and we want to target the most distant objects where a wider separation is needed?
Personal hotpost to the rescue!
Simply let one device connect to the other's device Personal Hotspot. This counts as normal Wi-Fi and the range is greatly improved, even though technically it's a direct phone-to-phone connection. The actual internet connection is not used in this application, the personal hotspot Wi-Fi connection is only used as a way to turn the close range Wi-Fi Direct connection into a long range Wi-Fi connection. (But be careful, some other applications or system services can start using the other phone's internet when connected this way)
Typical distances and how to reach them
Stereoscopic vision of a typical human is only effective up to about 50 meters (160 ft). Even the modest "close range" (no Wi-Fi) connection from 3m (10 ft) away gives us the 50 times wider stereoscopic base, increasing the effective stereoscopic range up to a mile or two. This is good enough for many architectonic and natural landmarks, and sometimes even the unusually low hanging clouds. Mountain ranges and regular clouds observed closer to the horizon are much more distant: 10-30-50 miles or more. This means that the distance between the "eyes" (persons holding the phones) should be at least 50m (160 ft). This can only be achieved by connecting both devices to the same Wi-Fi network or making one device use the Personal hotspot of the other device.
What is the maximum range?
Unknown. I personally managed to connect my iPad to the iPhone hotspot from about 100 meters away. I guess it was only possible thanks to being away from other Wi-Fi networks. So, don't count on such result in the city. Theoretically, the largest distances can be expected with a Wi-Fi connection through a router, or maybe even several routers serving a single network (as long as the configuration of this network allows direct connections between users). In the field, perhaps an ordinary mobile access point will give distances greater than a personal hotspot from an iPhone?