On another forum, somebody asked how a laser beam could reflect back accurately from the mirror the astronauts placed on the Moon.
The answer given from one responder was as follows :
There are two things that are less obvious and very important to understand why it works.
The first is that while laserlight is highly coherent and a small beam, it does disperse. By the time it reaches the moon it is about 200 meter wide. This makes aiming a little easier. Unfortunately it also reduces the intensity so catching a reflection requires decent sensitivity.
The second issue is that mirror is not what we use in the bathroom. As you correctly guessed a single flat mirror would reflect with the same angle, making it near impossible to hit it exactly right. But the same reflection makes that two mirrors under 90 degrees will beam back in the same plane. With three mirrors any beam will be reflected exactly to the source.
In a similar problem of finding small ships on the radar a similar reflector is used
I don’t get this two-mirror, three mirror thing at all, and in particular I don’t understand why three mirrors would necessarily send the beam back to source.
The mirror in the XY plane reverses the Z component of the light’s direction. The mirror in the YZ plane reverses the X component. And the mirror in the ZX plane reverses the Y component. So all three components are reversed, which means the whole beam is reversed.
This is a scene from The Big Bang Theory about this:
The timing of the reflection from the moon can be measured so accurately that we can know the distance of the moon at that moment within three centimeters and thus we can know the rate the moon is receding from the Earth to the nearest millimeter.
You can see this yourself with two vertical mirrors placed 90 degrees to each other. I’ve seen that in bathrooms on occasion, and as architectural features. Looking at such a configuration you will always see yourself with your face centered at the intersection of the two mirrors and at the same level
Add a third mirror and the orientation of the mirrors no longer matters. (I know I’m repeating information already posted, just wanted to recommend trying it out yourself.)
Sorry – I’ve been away, or I’d have weighed in sooner on this.
as others have properly stated, the reflector array on the moon consists of retroreflectors. In fact, as this site sets out, there are five different retroreflector sites on the moon – 3 left by the US (Apollo missions 11, 14, and 15) and two by unmanned Russian missions (Lunokhod 1 and 2)
The US ones have 100 0r 300 “corner cubes” (which look, as the name implies, like a corner cut off a solid glass cube, thus forming three mutually perpendicular faces,. These act like mirrors, even without a silvered coating, because of Fresnel reflection). The Russian ones only have 14.
There’s evidence that the corner cubes are deteriorating. This site has some info on it: http://www.skyandtelescope.com/astronomy-news/pesky-problems-for-lunar-reflectors/ It’s thought that the retroreflectors are being covered by dust and/or altering under solar heating and possibly other influences. In any event, the reflected returns are weaker now than they were in the past.
Just as a side note, there are several different kinds of retroreflectors (optical assemblies that send light back in precisely or nearly the same direction it came from). I devote a chapter to them in my book. The Corner Cube is one of the simplest designs and one of the more robust, but there are others easier to make or better fitted to different circumstances.
The Corner Cube was a surprisingly late development. It followed the invenbtion of the Penta Prism in 1864, which directed light at right angles to its original path, regardless of the prism’s orientation. The Corner Cube-type retroreflector , possibly inspired by this, was invented in 1887 by A. Beck, who called it a Tripelspiegel (“three-mirror”) or ZentralSpiegel (“Central Mirror”). But retroreflectors were restricted to specialty applications like rangefinding and the like. It wasn’t until night-time driving in automobiles became a big thing (with people needing to be able to accurately see markers at the sides of unfamiliar roads while traveling rapidly after dark) that retroreflectors became a mass-produced and marketed item, and they used other types before they finally hit upon designs base on the corner cube as the cheapest and easiest to produce.
Good idea: That way, it doesn’t matter which way you hold your shield, Medusa will still end up seeing her own reflection and petrifying herself. And it works for death rays, too.
And the corner cube is the cheapest and easiest to produce for some applications, but not for all. There’s also retroreflective paint, for which sphere reflectors are used, because it’s easier to apply as a random coating.
Yes, that’s one of the other methods. It’s not as efficient as corner cubes, but very easy to apply.
As for Medusa, the idea of her seeing herself in the shield and petrifying herself has appeared, but it’s a relatively recent idea, only showing up in the last few decades, just like the idea of a Medusa with a snake body. Never heard of anyone using a retroreflector on her, though. It’d have to be a big corner cube to throw the entire image back at her, of course. And the image would be upside-down.
Got me thinking … on a theoretically perfect snooker table, with a theoretically perfect ball, and a theoretically perfect initial strike, will the path of the ball when struck into a cushion so that it hits four cushions describe a parallelogram, so that it always returns to the initial spot? Or do the dimensions of the table, and the initial placement of the ball come into play ?
As you can probably tell, I am not a pool shark … and for the purposes of the question, let’s assume the table has no pockets …
Thread drift, I realize, but hardly worth a fresh thread IMO , and it is kinda analogous to the light reflection thing …
That depends on what qualities you deem “perfect” for a pool ball and table to have. Is a theoretically perfect pool table the same as a theoretically perfect air-hockey table? Rolling is different from frictionless sliding.
Even with a perfect air hockey table, though, it won’t necessarily return to the initial spot. In fact, for any given table dimensions, for most angles it won’t ever, and even if it does, it usually won’t be a single parallelogram. For a simple example, picture a 1x2 table, with the ball starting close to a corner, and hit at a 45º angle: The full path then will be close to a V shape.
I believe that for any triangle you can find a path that strikes each side once, returning to its original starting point. If you shift the starting point a little and send your ray parallel to the initial one, you generate an “orbit” that returns to its starting point after two turns around the triangle. In general, though, any random path is not guaranteed to close on itself.
In a square or rectangle, since the corners each act like a two-dimensional corner cube you will can repeating 'orbits", too.
I think that you can get something similar happening in a parallelogram, but it’s not guaranteed to return to its starting point. You can demonstrate this by “unfolding” the reflections from the parallelogram to cover a plane.
And it’s interesting to note that the basic cube corners with all planes meeting at a 90 degree angle are so good at returning the light parallel to the incoming direction that most modern retroreflectors used for night time driving applications actually use “cube corners” that are deliberately deviated from 90 degree intersections, since the source of the light (the headlights) isn’t actually where you want the reflected light to go, which would be the driver’s eyes. There’s a host of patents out there for designs that try to optimize a reflector pattern that directs the light to the driver.
A simple glass bead is a pretty good retroflector, and that’s how the reflective lane markings are made - when the paint (actually a thick, molten plastic) is laid down and still sticky, the workers sprinkle handfuls of tiny glass beads on top of it. Fresh lane markers are amazing - they will reflect headlights from a mile or more away. The beads eventually wear away, but even after many years, enough remain to make the markings reflective.
And if you walk down the road just after they sprinkle those beads, you’ll see rainbows at your feet. It’s the same principle as a rain rainbow, just with slightly different angles.
Simple enough to prove. You just need one angle that hits to the left of your initial point and one that hits to the right, and then it’s just the intermediate value theorem.
Well, actually, the glass bead by itself is a terrible retroreflector – the refractive index required to make the Fresnel reflection from the back surface is a bit high for glass. You can make up for this by making your glass bead from hemispheres of two differently-sized spheres, which is how the first retroreflector patented for use on roadsides was made.
Unfortunately, that requires casting them to a specific set of measurements.
the stuff that’s used on white line markers that you’re talking about works in a different way. The spherical glass bead acts like a really short-focus lens to take incoming collimated (or, usually, quasi-collimated) light and almost focusing it on the white paint that the sphere is resting in. The light diffusely reflects from that white paint surface in all directions, but quite a lot of it gets re-quasi-collimated by the glass sphere in the direction it came from.
It actually works quite well, for such a sloppy optical system. It’s an easy enough experiment to get yourself a sheet of paper, a gluestick, and some tiny glass beads from a craft shop. Use the glustick to leave a trail of glue on the paper, sprinkle the glass beads on it so they stick, then put your eye close to a flashlight pointing at the beads, and watch them “light up”. It’s even more impressive if you put the beads on top of fluorescent paper and illuminate it with an ultraviolet flashlight.
Sometimes in nature you get early morning dew suspended on hairs on grass blades, in which case you can get an even better effect because the grass isn’t in contact with the spherical droplet, but it about at the focus of the droplet lens, so the retroreflected light is even better collimated. The effect is called heiligenschein. Looking at your shadow cast in such dew-covered grass at sunrise gives the impression of a halo around your head – and only your head. If you’re with companions, their shadows (to you) don’t appear to have such halos.
Onescientist observed a similar effect from droplets on pine needles and the like, and called the effect sylvanshine.
