I recently participated again in the annual UNCC Science and Technology Expo, showing off neat science demos to the public. This year, I decided to add a table of “Optics and Illusions,” to show how science and our own brains can be used to trick us. Of all the cute tricks I showed, however, none was as popular as the Mirascope that I purchased for $9!
The device produces a clever optical illusion; I recently purchased a slightly larger version of the Mirascope, and a video of it in action is below. (Apologies for the quality; I had a hard time trying to focus on the image. I’ll post a better video as soon as I can take one.)
A small object placed within the device produces an image that appears to hover right over the central hole. The video does not even do the effect justice; it is really something one needs to see for oneself. Both the Mirascope and its larger competition bill themselves as “holograms,” though the effect is not a true hologram in any sense of the word! Rather, it is a clever implementation of simple geometrical optics. Explaining how it works is an excellent opportunity to talk about some basics of light propagation, and how light forms images.
So what is “geometrical optics?” In almost all of our ordinary experiences with light, it acts like a stream of particles, traveling in straight line paths unless it bounces off of a reflective surface (reflection) or passes across an interface between two media (refraction). Thanks to things like sunlight peeking through clouds (as in the image below), for a long time our view of light was as a collection of rays.
We have known since the early 1800s that light has wavelike properties as well, but it requires carefully prepared experimental arrangements to clearly see wave effects. In fact, it is fair to say that the ray description of light was almost completely unquestioned for some 2000 years.
During that time, the laws of reflection and refraction were used to describe and design basically all optical devices. The law of reflection says that the angle of reflection is equal to the angle of incidence .
The law of refraction, which we have discussed quite often on this blog, may be written in mathematical form as:
Where and are the refractive indices of two media, and the angles are given in the following image.
We won’t worry about the details of the law of refraction, as the mirascope we’re concerned with in this post uses reflection!
The law of reflection allows us to determine the image-forming properties of a spherical mirror. For instance, in the illustration below, we use two light rays from an “object,” combined with the law of reflection at the mirror itself, to determine the position, size, and inversion of the image.
There are, in fact, two ways to find the image of a spherical mirror. We can use the law of reflection to determine the direction that the rays reflect off of the mirror (the orange lines help with this), or we can use the focal point of the mirror to make things easier. It can be shown that every light ray that passes through the focal point will reflect off of the mirror horizontally, and every ray that hits the mirror horizontally will pass through the focal point. Drawing two rays is typically sufficient to find the image point.
The result is what we call a real image: the image formed by the mirror actually exists in real space as a place where light rays intersect. Real images are the basis of the Mirascope, as well as other clever illusions: in a previous post, I’ve shown how one can create a “phantom lightbulb” using them.
Historically, a real image even, inadvertently, terrified a king! In the early 1700s, an optical glassmaker named Villette became known for his gigantic, high-quality, spherical mirrors, which he sold and presented to royalty throughout Europe. As described in an 1855 memoir:
They had also, of course, their optical effects. The figure reflected from any concave mirror apparently stands out from its surface, just as the figure reflected from a convex mirror seems to be contained within it. When one of these instruments was presented to the King of France — Louis Quatorze — his majesty was requested to draw his sword and thrust towards the burmished surface. He did so; and because, at the same instant, his image appeared to leap forward and direct a thrust at his own face, the great monarch recoiled in alarm, and was so much ashamed of himself directly afterwards that he would see no more of the mirror for that day.
This brings us to the Mirascope! The device is simply two approximately spherical mirrors ¹placed facing each other, as seen opened up in the photo below.
We can see how the device forms its illusory image by using the law of reflection, as above. (The system is too complicated, as far as I know, to describe by using focal points.) My rough sketch of the illusion is shown below, using the actual cross-section of a Mirascope as a guide.
I’ve drawn two sets of rays from the object frog to the image frog, in orange and blue. I did this so that we can see which way the image faces, as well as where it appears. As you can see, light that illuminates the frog then bounces twice — once on the upper mirror, once on the lower mirror — before forming an image at the top of the device.
You can find this description of the Mirascope in a lot of places on the internet (though the diagrams aren’t as pretty as mine). As an optical physicist, however, I would like to do a little better! When you look at the illusion, you will note that it only works for a finite range of angles. If you look at the image from directly above, you only see the object right below, obviously; if you look at the image too far to the side, it also disappears. Can we use geometrical optics to explain these limits?
The diagram below shows the limitations. I’ve simplified the object to be just a simple arrow for illustration. The blue and orange rays in this picture represent the extreme rays that can be seen as part of the illusion. The blue ray is the steepest ray that can leave the object and be reflected by the upper mirror and not just leave the aperture. Anyone looking at the Mirascope from an area higher than the blue ray coming out of the device will just see the object directly. The orange ray is the lowest ray that can leave the object and not be obstructed by the upper mirror after the second reflection. The pinkish region shows, roughly, the area from which one can see the illusion.
In other words, look at the illusion from too shallow an angle, and the rays get cut off by the upper mirror; look at the illusion from too steep an angle, and the rays never get reflected by the upper mirror in the first place! The size of the hole, in the end, dictates what angles the illusion is visible from.
The Mirascope has a curious history, and was in fact discovered by accident². Around 1969, a custodial worker named Caliste Landry was cleaning large surplus searchlight mirrors from World War II in the UC Santa Barbara physics department when he noticed an illusion of “dust that couldn’t be cleaned.” He shared his observation with a faculty member, Virgil Elings, and the two of them applied and were awarded patent US 3647284 A, “Optical display device.” The first image from the patent is shown below; you can see essentially the same ray-tracing depiction of its operation that we described above.
So the Mirascope forms an image using simple mirrors, and not by some sort of hologram as the box claims. The confusion is understandable, however, as most people have come to understand the word “hologram” to mean “three-dimensional image,” though the term has a much more specific meaning to optical physicists. The famous Pepper’s ghost illusion — of which I will have much to say in future posts — is often confused for a hologram as well. We should end this post, then, by explaining a little bit about holograms.
A hologram is, in short, a photographic recording of a three-dimensional image. When this photograph is illuminated by a light source such as a laser, it reproduces the original recorded three-dimensional scene. Unlike the Mirascope, which can be explained by treating light as geometric rays, a hologram is fundamentally a wave phenomenon.
An illustration of this (taken from my upcoming textbook) is shown below. The hologram is recorded as shown in (a), with coherent laser light both directly illuminating the photographic film as well as the object to be recorded. When the processed film is reilluminated from the same direction, a three-dimensional virtual image of the object appears in its original location.
How does it work? A photographic film typically only records the intensity, or brightness, of the light incident upon it. Light not only has an intensity, however, but a direction, known as “phase” in terms of waves. If we could somehow encode the direction of light on the film as well as the intensity, we would then see the full three-dimensional picture.
The key is to interfere two waves together on the photographic film, producing an interference pattern of bright and dark bands, as in Young’s double slit experiment. The interference pattern has the direction of light we need encoded in it; this is why we create a hologram by interfering light that directly hits the photographic film with light that hits the object.
The hologram process isn’t perfect. As can be seen in my hologram image above (in what is known as the Leith-Upatnieks configuration), a second real image is always created in the recording process. By tilting the photographic plate at an angle to the illumination, however, we can make sure that the virtual image and the real image don’t obscure each other.
If this description sounds confusing, don’t worry — it is quite difficult to explain holograms without delving into the mathematics of wave interference and photographic recording! If you take anything away from this, however, it should be this: the Mirascope is a geometrical optics effect, while a hologram is a wave optics effect.
The labeling of the Mirascope as a “hologram” may be considered a bonus illusion that comes with the device!
¹ Strictly speaking, the mirrors are parabolic, but the device is small enough that they are approximately spherical.
² Sriya Adhya and John Noé, “A Complete Ray-trace Analysis of the ‘Mirage’ Toy.”