I found this object a couple of months ago, prominently poised on a rock in the broken ground above the big bulldozed path on Beinn Bhuidhe. (Yes, I do occasionally climb a hill without telling you about it.) It was marked with rainwater and bird droppings, but cleaned up remarkably well once I got it home.

It’s a signalling mirror, of a very particular variety that I’ll come back to later, but I suspect from its location that whoever lost it had been using it as a more conventional mirror—adjusting an errant contact lens, perhaps, or making sure they’d rubbed in their sunscreen evenly.

Signalling with a mirror is a very slightly technical exercise. Movie characters can simply pluck up a random bit of broken glass and us it to attract the attention of a passing helicopter in short order. But the problem lies in knowing where the reflected beam of sunlight is going—easy enough to flick a spot of light around on a nearby wall, but how can you direct it specifically towards a target moving across the empty sky?

The simplest solution is to direct the sunlight on to something nearby which you have aligned with the distant object of your signalling. Hold up two fingers at arm’s length, frame the object between your fingertips, and use the mirror to reflect the sunlight on to your fingers.  Simple!

The problem with this approach is (as my diagram shows) that the mirror is off your line of sight—the line from your eyes to your fingers extends to the helicopter, but the line from the mirror to your fingers doesn’t. So you need to keep the mirror as close as possible to your eyes, and your fingers as far as possible from your face, in order to minimize the angular error. If you place the mirror directly below your sighting eye, then the error will be in an upward direction, so painting the reflected spot up and down the length of your fingers should ensure that your target receives an intermittent flash.

So, the next elaboration is to use a purpose-built mirror with a hole in the middle. That way, you can look through the hole at your framing fingers, and know that when the fingers are illuminated, the distant helicopter is, too. In practice, this is a little tricky—once you’re peering through the hole in the mirror, the limited field of view makes it difficult to find the reflected spot of light and direct it on to your fingers.

What we need is some way of telling by looking at the back of the mirror where the reflected light is going. Then we can dispense with the fingers, and simply look through the sighting hole at the target while steering the reflected beam towards it.

The simplest way of doing this is using a double-sided mirror with a hole in the middle. When you hold it up to the sun, it casts a shadow with a bright spot in the middle, corresponding to the hole. This shadow may be projected somewhere on your body, if the sun is roughly ahead of you, but it may be off to one side. The first thing to do is to find that shadow and its bright central spot—you may need to hold a hand out to one side or the other. Next, tilt the mirror so that you can view the mirror’s shadow and central spot reflected in the back surface of the mirror. Next, align the central hole in the mirror so that you can see your distant target through it.

Got all that? Good. Now gently adjust the tilt of the mirror (without letting the target slip out of view in the central hole) so that the reflection of the mirror hole seen in the back of the mirror disappears into the hole in the centre of the mirror, superimposing it on your target.

You end up with light reflecting along equal and opposite paths from the front and back of the mirror, as shown above. Simple geometry now guarantees that your reflected light beam is striking the target.

Here are some photos which may make the process clearer. I use a Deutsche Grammophon CD for this purpose, because their top surface has a mirror finish, providing me with a ready-made perforated double-sided mirror.

Here’s the CD. You can see my shirt (and camera) reflected in its back surface, and the shadow of the CD is on my shirt at the lower right rim:

Now I’ve tilted the CD to make the shadow entirely visible, with the reflected image of its bright central spot directly above the hole in the CD:

All I need to do is to steer the bright central spot into the hole in the CD, and the other side of the CD will be reflecting light towards whatever I can see through the hole. Below, I’ve got the reflected hole superimposed on the real hole, and through the hole you can make out the bright spot of light projected on to the building beyond:

This is the sort of signalling mirror that was provided in life-boats during World War II, except the sighting hole was small and cross-shaped for accurate use. Here’s the instructional video, which lets you see the device in action:

Still a bit of a palaver though, isn’t it? The next step in the development of the signalling mirror came just after the war, with the incorporation of retroreflective beads into the design. Retroreflective beads work in the same way raindrops do when they form rainbows. Light from the sun enters the drop, is refracted, reflected and refracted again, and so comes back out of the drop at an angle of about 42º to the direction at which it entered.

The higher the index of refraction, the closer the light comes to bouncing straight back where it came from—retroreflection.

In practice, retroreflective beads generally have a reflective coating at the back, which allows the reflected light to be coloured and scattered over a reasonably wide viewing angle, and also allows the use of cheaper glass with a lower refractive index. In this form, they’re used to coat the surface of road signs and those reflective safety garments that appear to “light up” in the headlights of your car.

The little mirror I found has retroreflective beads distributed in a grid around the sighting hole in the corner. I can show them up if I take a flash photograph at an angle to the mirror surface—the beads suddenly glow brilliant white:

So the beads around the sighting hole are reflecting the sunlight back on itself. How does that help? Well, there’s a layer of glass across the front surface of the sighting hole, and a small proportion of the retroreflected light will bounce off the back of the glass, pass through the holes in the grid that supports the beads, and arrive at your eye as you view the back of the mirror. This gives you a little spot of light (a faint doubly-reflected image of the sun) at the edge of the sighting hole, which you can move around by tilting the mirror. Tilt the mirror until the spot is central in the sighting hole, and you’re looking directly down the beam of sunlight being reflected from the mirror on the other side. The geometry looks like this:

Here’s my best shot at showing you what it looks like. My found mirror turned out to be pretty rubbish for this purpose, so I’m using one of my own.

The retroreflector beads are distributed in the ring of small holes around the central sighting hole. It’s impossible to get a camera close enough to the sighting hole to show the full effect, but you can see that the lower three holes in the ring are brightly illuminated by the sun, whereas the rest are dim. If I move my eye in close to the sighting hole, that patch of bright illumination remains the same angular size, and so resolves itself into a small bright image of the sun, positioned in one of the ring holes. Then, by tilting the mirror, I can steer this bright image into the central sighting hole. In the image, the mirror needs to be tilted back slightly, to lift the reflected light into the line of sight.

This arrangement, patented by Richard S. Hunter in 1946, finally gives you a signalling mirror you can always use with one hand. Which is pretty useful if you’re injured, or trying desperately to hold the bow of a lifeboat into the oncoming waves.