Pehr Sällström
Mirrors, Virtual Images and the Holographic Pyramid
Version date 2021-06-09
VIDEO se https://youtu.be/YG4bzGNc1E0
VIDEO uk https://youtu.be/v4EdhG4D_T0
Ingress
I see myself in the darkness of my tablet...
But also the window .. behind ..
My line of sight is redirected, so that I see things that are behind me.
Mirrors always show us something else than what we think we are looking at.
Framed pictures may under circumstances show you quite another view than the depicted one.
Let us play, for a while, with mirrors!
An ordinary mirror may seem simple .... but is an intriguing optical device. Produced with technological skill as an implementation of the idea of a perfectly plane and smoth highly reflecting surface. Here I have mounted one, in an upright position on a table.
An object on our side gives rise to its virtual counterpart, seemingly as far behind the mirror as the object is on our side. They hang together.
What gives this optical illusion a character of reality is the fact that the position of the object is independent of the direction and position from which I observe it. If I move, it doesn't move.
The logic of mirrors can be clarified by help of the wonderful science of geometrical optics. My visual intention is directed straigt forward, and can be symbolised by "rays of sight".
The mirror makes a deceptive impression of transparency. In reality it is completely opaque. Whatever is behind, is secret.
Instead my view is redirected so that I see things behind or at the side of me. But how is that? The mirror can't influence my vision - can it ?
As a physicist I prefer to discuss the issue ... not in terms of vision, but in terms of light-rays, originating at the object, and being reflected at the surface of the mirror, according to the simple rule: the angle of reflection is the same as the angle of incidence. Some reflected rays reach the eye of the observer.
If the observer changes position it doesn't matter. The rays entering his eyes will seem to originate at one and the same point. Namely the point where the virtual object is localised for his sight.
But this must be an illusion? What I see is actually the candlestick, here, on this side.
Well it is a bit more intriguing.
I ignite the candle. Immediately the virtual candle behind the mirror is also ignited. I reduce the general illumination of the scene.
Now, let us introduce a shadow casting object. What is remarkable is that you get two shadows. One is casted in the light from the real candle, the other one in a flux of light apparently coming from the flame behind the mirror. Shining right through it!
Paradoxically the virtual flame illuminates the scene from its position, as if we had to do with two flames.
You may prefer to call the candle behind the mirror an illusion. But from the point of view of optics it is a virtual image and - in a sense - as real as the material one. You have a situation with two light sources, at some distance from each other, both sending out a flux of light.
We could put a real candle there, behind the mirror, exactly in the position of the virtual one. Take away the mirror -- And optically it would be the same situation.
So, again, what is it I see? I see that radiant flame behind the mirror - not the one here, beside me. Or, rather, I see both simultaneously. They are there, both of them. One shaped out of matter, the other one weaved of light.
The flame we see through the mirror is no illusion, but an objective phenomenon. An optical entity. Only not material.
Two comments should be made here. One is that Vasco Ronchi, in his book "Optics -The Science of Vision", has rightly pointed out that the mirror image you see in a distant mirror does not appear to be as far behind the mirror as the object is in front of it. Rather almost in the plane of the mirror. Compare with the rainbow, in a natural scenery. It seems to be where the rain falls.
The other comment concerns the fact that the virtual flame functions as a secondary, in certain respects independent, light source. This is used e.g. in a digital projector with separate channels for R, G and B. It is enough with one lamp, the other two can be mirror images of it. The light energy comes of course from the real lamp, and is effectively used in this way.
Remember also Fresnels demonstration of the interference of two fluxes of light, with the help of a double mirror, creating two virtual sources out of one real.You cannot get interference with two separate real light sources, because they need to be coherent. Or even, as Paul Dirac says more incisively: "each photon interferes only with itself".
A TRANSPARENT WINDOWPANE
It is perhaps unsatisfactory not being able to see what is there, in the space behind the mirror. Well, a mirror need not be opaque, as we saw in the beginning, with the framed picture. So let us use an ordinary window pane like here.
Nothing behind .. until you see it from this side .. then the virtual candle is there.
Again I ignite the candle and lower the room illumination.
If a put the cork in place, we see only one shadow. The reason is that the reflectance factor of the glass plate is low. Hence we do not see the shadow casted by the light coming from the relatively weak virtual flame. This is the price we have to pay for transparency.
Light is reflected both at the front and the back surface of the pane. About 4% at each one, so 92% passes through. The previous mirror, with silver coating on the back, gives rise to multiple images by this reflectance to and fro, as you can see in this photo.
The degree of reflexion depends on the change of index of refraction (in this case between air and glass). A way to accomplish anti-reflex is to make the transition soft (gradually changing index) which means: the glass surface should not be a mathematically perfect plane! The idealization of the mirror creates the problem of multiple images.
Anyhow, with a transparent mirror we can do something else -- let me turn the glass plate like this.
Now the real candlestik kan be moved to the side, even out of sight. Only the virtual flame is seen, ghost-like, on the other side of the window.
In terms of geometrical optics the situation is as follows. The real candle may be hidden. But still it can intermingle with the real objects in the world behind the window .. like this.
THEATRICAL GHOST APPLICATION
Another application of the same idea is shown in this engraving. It is a trick to make a ghost appear onstage.
I couldn't resist the temptation to try this out in reality. Let be in puppet theatre format.
On the web you can find "hologram ready" videos with dancing figurines on black bakground.
Here I have arranged a scene for a couple of them. Let them dance!
THE HOLOGRAPHIC PYRAMID
On Youtube you can also find examples of a more advanced variant, namely a four sided pyramid. It makes it possible to see the dancing figure from four sides.
Again, a bit of geometrical analysis. The sides of the pyramid are sloping 45 degrees to the floor. In the ceiling you find the moving pictures of the figur.
By adjusting positions one can make the figure stand at the center of the pyramid.
How do I make such a "holographic" pyramid? First I have to measure the width of my screen. Half of it takes me to the center, under the top of the pyramid. The height of this should have this same measure.
Each side of the pyramid is a triangle with the following measures. Make a template in thin cardboard and use it to cut out the four sides from a thin sheet of polyester.
After some constructing efforts you have the mini theatre.
And so Luka can continue dancing.
FINALLY: WHAT IS IT WE SEE?
So, again, what is it we see? We see the figurine, in the transparent pyramid. If we try to go inside and touch her - she is not there. It is as with the rainbow: you cannot reach it. We do not see a lot of mirror images of the sun in the waterdrops, forming the bow. No, we see just the rainbow. A virtual entity. As such it is objective, not a subjective illusion.
The dancing figurine may have something to tell us, with her dance. Like the virtual flame, behind the mirror, which could take part in a play of shadows on our side of the mirror.
*
| LIST OF TEXTS |