In a recent Jocko Podcast on the Boer War, he and Echo wondered aloud about how big a signal mirror would have to be to be seen at 40 miles. Not that big, it turns out:
Most heliographs were variants of the British Army Mance Mark V version (Fig.1). It used a mirror with a small unsilvered spot in the centre. The sender aligned the heliograph to the target by looking at the reflected target in the mirror and moving their head until the target was hidden by the unsilvered spot. Keeping their head still, they then adjusted the aiming rod so its cross wires bisected the target. They then turned up the sighting vane, which covered the cross wires with a diagram of a cross, and aligned the mirror with the tangent and elevation screws so the small shadow that was the reflection of the unsilvered spot hole was on the cross target. This indicated that the sunbeam was pointing at the target. The flashes were produced by a keying mechanism that tilted the mirror up a few degrees at the push of a lever at the back of the instrument. If the sun was in front of the sender, its rays were reflected directly from this mirror to the receiving station. If the sun was behind the sender, the sighting rod was replaced by a second mirror, to capture the sunlight from the main mirror and reflect it to the receiving station. The U. S. Signal Corps heliograph mirror did not tilt. This type produced flashes by a shutter mounted on a second tripod (Fig 4).
The heliograph had some great advantages. It allowed long distance communication without a fixed infrastructure, though it could also be linked to make a fixed network extending for hundreds of miles, as in the fort-to-fort network used for the Geronimo campaign. It was very portable, did not require any power source, and was relatively secure since it was invisible to those not near the axis of operation, and the beam was very narrow, spreading only 50 feet per mile of range. However, anyone in the beam with the correct knowledge could intercept signals without being detected. In the Boer War, where both sides used heliographs, tubes were sometimes used to decrease the dispersion of the beam. In some other circumstances, though, a narrow beam made it difficult to stay aligned with a moving target, as when communicating from shore to a moving ship, so the British issued a dispersing lens to broaden the heliograph beam from its natural diameter of 0.5 degrees to 15 degrees.
The range of a heliograph depends on the opacity of the air and the effective collecting area of the mirrors. Heliograph mirrors ranged from 1.5 inches to 12 inches or more. Stations at higher altitudes benefit from thinner, clearer air, and are required in any event for great ranges, to clear the curvature of the earth. A good approximation for ranges of 20–50 miles is that the flash of a circular mirror is visible to the naked eye for 10 miles for each inch of mirror diameter, and farther with a telescope. The world record distance was established by a detachment of U.S. signal sergeants by the inter-operation of stations on Mount Ellen, Utah, and Mount Uncompahgre, Colorado, 183 miles (295 km) apart on September 17, 1894, with Signal Corps heliographs carrying mirrors only 8 inches square.
Just don’t try to use it during hours of darkness.
Some say the Great Wall(s) of China could have been used as a heliographic network. Heliography is an ancient technology.
Ezra: true darkness is a problem, but sun is optional. Signalling by moonlight was practiced by many, and I’ve seen one account where it summoned help in desperate circumstances. Here’s a citation from 1880:
“Signaling by moonlight with the heliograph has been practiced during the last two years on service, and it is hoped that the results will soon be published. I have tried it on two different occasions; first in the Jowaki campaign between General Ross’s standing camp and the Sargasha Ridge, and subsequently between Jutogh and Subathu, distant 12 miles. The signals were intelligible in each instance, but the heliographs and telescopes were set up by day and remained in position till the moon rose, otherwise it is doubtful whether the alignment could have been hit off, unless signal fires had been used. At the time communication was established between the Cabul and Kuram Valleys, advantage was taken of a full moon, and a heliograph set on Kuram from the Agam Pass. The light was seen with the naked eye 12 miles off.
https://books.google.com/books?id=40bOAAAAMAAJ&pg=PA485&lpg=PA485&dq=moon