MIRROR

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1.  Optics

 

The optical experience inside a hemispherical mirror is unique. Such a mirror allows the formation of "real-images".  These images hang in space in a completely three-dimensional fashion. This means that an observer can walk completely around such an image, observing parallax; that is, the relative motion of images different distances away.  These images look exactly like the objects they represent so that the real and image worlds cannot be distinguished.

 

The difficulty of distinguishing mirror reflections from real objects is familiar with a good plane mirror.  The only way its presence can be detected is by an attempt to reach through it.  The images in a plane mirror exist in a space on the other side of the mirror.  This is the phenomenon which makes a room look bigger when one wall is covered with mirrors.  The plane mirror generates an image world which is called "virtual", since it exists in a "virtual" space behind the mirror.  The virtual image world is right-side-up or "erect".

 

The spherical mirror produces an image world which is much more complex than that of a plane mirror.  Most dramatic is the "real" image world which exists in "real" space inside the dome.  These images are up-side-down or "inverted" but otherwise cannot be distinguished from physical reality since both the real image world and the real physical world coexist in the same space.

 

Figure HI diagrams the way in which these real images are formed.  Assume the spotlights light only one man in the Pavilion. Then all people in the Pavilion (for example, the woman) see his image floating upside down in space above them.  Just as with a plane mirror the light which scatters off the man and his clothing reflects in the mirror.  The spherical curvature of the mirror surface, however, causes a focusing of these light rays (see Fig. HI) into the space inside the dome.

 

It is easy to construct  diagrams like these utilizing the law of reflectivity:  the angle of incident equals the angle of reflection.  This law is true for all mirrors independent of their shape when each light ray and each local part of the mirror is considered  independently.  This law means that both the incoming and reflecting light rays make the same angle with the mirror surface.

 

Because the man's real image actually hangs in space, the woman can walk entirely around it on the floor while looking up.  In this way she verifies that his image does indeed exist inside the space of the dome.  The focusing distance of her eyes or of a camera also determines the position of the image.

 

One unique property of these images is their individuality. That is, each person on the floor sees the real image of a particular person or object appearing to hang. in space in a slightly different position.  The technical reason for this is a spherical aberration:  This means that different parts of a large spherical mirror reflect images to different positions. Such a phenomenon is shown in Figure H2 where the illuminated man sees his own image smaller and lower down in space than his image which the woman sees.

 

It is important to realize that light rays cannot be seen unless they enter your eye.  This same property of light was also discussed in the Light Frame section where it was mentioned that those light beams were visible only because of scattering of suspended particles in the air.  This means that the image which the man sees, the small, lower one, will not be seen at all by the woman. The light rays which form that image return only to the eyes of the man, or people standing near him.  Similarly, the man's image which the woman sees is her personal one--the light rays which form it enter only her eyes.

 

If there were no spherical aberration, and all light rays in the dome formed a single real image, scattering by suspended particles, smoke, or a translucent screen would make this image generally visible to all people in the room.  A ground glass screen in a reflex camera, for example, makes the image of the camera lens generally visible.  In this hemispherical mirror, since each light ray forms a different image, ground glass reveals a blur of light, the result of many out-of-focus images, rather than a single well-focused image.

 

Spherical aberration means that if many people on the Pavilion floor point to the same man's image, they will find they are pointing in different directions.  This fact, when appreciated by the observer, lends an air of uniqueness and individuality to his images.  No two people can have exactly the same image world.

 

These facts have been Incorporated into diagrams of typical image worlds.  No one diagram can represent the entire image world which is composed of an infinity of7private worlds, each person in the Pavilion requiring his own diagram.  Diagrams H3-5 show three typical image worlds for three typical observers.  In all three cases the observer is distinguished by being the only woman.

 

The diagrams portray the real images produced by light reflecting once from the mirror.  Beyond this image world are other real image worlds produced by light reflecting two or more times in the mirror.  With a good quality mirror surface many additional reflection image worlds will be created.  These will appear in rings surrounding the primary image world.  How many you see depends on where you stand, the lighting, and the optical quality of the dome.

 

Below the real image worlds in the mirror appears a band of pure light, relatively bright, with no image in it whatsoever. When you look in that direction it not the mirror which you see or images, but pure light.

 

If no people were standing in the outer half of the sphere, the band of pure light would extend all the way to the bottom of the mirror.  If illuminated people stand near the mirror, however, their enlarged erect virtual images can be seen in the mirror. That means people, right-side-up, larger than life, appear to be on the other side of the dome, in imaginary space.  This magnifying "virtual" image world is familiar  to everyone who looks in an ordinary magnifying cosmetic or shaving mirror.  These magnifying mirrors are spherical mirrors just like the Mirror Dome, but are very small segments of the total sphere.  The amount of magnification of such a mirror depends on how close you are to it.  As you move your face back away from the cosmetic mirror, the magnification increases; but your face's image also recedes into the distance behind the mirror.  Eventually your image will grow to fill the mirror.  This "infinitely" large image is "infinitely" far away through the mirror.  Beyond that point if you continue to back up, you will see only pure light in the mirror until you have backed away so far that you see yourself as a real image.

 

In Figure H6 the virtual image world is diagrammed demonstrating where and how large the erect virtual images appear to be. Only people in the outer half of the sphere produce virtual images, images which are seen by everyone.  The girl in the figure is standing half-way from the center to the edge of the dome.  Her image is infinitely large and infinitely far away.  Anyone standing closer to the center than she, will have no virtual images.

 

A unique experience occurs at the center of the spherical mirror; no matter where you look into the mirror, you see only yourself. If you are brightly lit, you cannot see any other parts of the floor as images.  You see all your own images and, in fact, no one else can see them but you.  Your image world is filled solely with yourself.  The exact center is the only place where you can exclude others from seeing your image and exclude them from your image world.  This egocentric viewpoint is unique to a spherical mirror.

 

2.  Construction

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The spherical mirror is the largest ever made.  Ninety feet in diameter, it is more than a hemisphere, subtending an angle of 210°, which means that the sides of the mirror extend 11 feet below its equator.  The mirror is an air structure. This means that it is made of a pliable film whose shape is maintained by air pressure.  This mirror is made of melinex, a plastic film, one-half of a thousandth of an inch thick. The mirrored inside surface is produced by vacuum~depositing aluminum on the film.  The outside surface is coated with a fire retardant adhesive.

 

Usual air structures use air pressures greater than an atmosphere inside the structure.  This particular structure, however, is double-walled with a slight vacuum between the two walls.  Behind the mirror is a steel frame, something like a birdcage, with a backing of wooden panels attached to it.  Behind all this a plastic cover fits loosely to make an air-tight seal.  This frame supports the vacuum.  The aluminized melinex is cut arid taped in gores to a spherical shape with a diameter smaller than that of the birdcage structure. Then a vacuum sucked behind the mirrorized balloon tends to pull it out into a spherical shape.

 

If the usual principle of a balloon had been followed, air would be blown into the mirror dome so that it contained more air than outside.  This would have necessitated revolving doors to maintain pressure when people walked in.  The double walled air structure eliminates this necessity and doors and windows can be as large and open as desired.  The mirror is tethered to the support frame at the three light holes.  A strong cord running through the bottom rim of the spherically shaped balloon provides an edge which is bolted to the floor with a special fastener.

 

The spherical surface is composed of 72 gores each 48" wide whose sides are lines of longitude.  The polar cap is an area 6 feet in diameter of specially strengthened material. Good optical properties necessitated careful fabrication.  A full-scale template cut to an accuracy of from 8 to 15 thousandths of an inch guided the cutting of the gores, one at a time.  The gores were taped together with an accuracy of 30 thousandths of an inch.  Because of possible creasing and scratching damage, the melinex film was sandwiched between thicker polyethylene during handling.  Careful packing for shipping and special erection were required.

 

The vacuum is maintained by a blower capable of 1000 cubic-feet per minute in free air.  A second unit is a spare to be used during maintenance.  Automatic pressure switches switch the blower on and off to maintain the desired air pressure.  Less than a thousandth of an atmosphere of air pressure is sufficient to maintain good spherical optics.  This is a negative pressure of 3/8" water.