STAIRCASE GELB EFFECT
Instructions

Alan Gilchrist

Brief description of the effect: A square piece of matte black paper is suspended in midair and illuminated by a bright spotlight. It appears white. Then a dark gray square is introduced into the beam of light, next to the first square. The second square now appears white and the first square appears very light gray. Then a third, middle gray square is added, and both the first and second squares appear darker still. A fourth light gray square is added, and finally a fifth white square. Each time a new square of higher luminance is added, it appears white and the other squares appear as a darker shade of gray. But even when all five squares are present at the same time, a pronounced illusion is still present. The first square now appears middle gray, even though it is completely black, physically. And although the five square now span the entire range of grays from black to white, they appear to span only a range from middle gray to white.

Basically the illusion is quite simple and, when set up properly, very robust. But there are several pitfalls that can weaken or spoil the effect. And the lighting conditions are different from room to room. The troubleshooting section should provide solutions to all these problems, but it is strongly recommended that you allow plenty of time to set up the demo and conduct a dry run well before you plan to show it before a group. Even with a lot of experience with this demo, I still allow about an hour for the set-up, mainly because it is a bit embarassing when the audience arrives in the middle of your preparations.

There are three basic components required for the demo: (1) a set of matte achromatic papers, (2) a projector, and (3) some mechanism for presenting the papers successively in adjacent positions.

PAPERS
One could use Munsell papers, but they are standardized papers and very expensive. There are several kinds of screen-printed gray papers available in art and drafting supply stores. I use Color-Aid brand. It comes in sheets 20" by 24", cost perhaps 3 or 4 dollars each. The surface of the paper must be very homogeneous and very matte. Construction paper, for example, will not work for the demo. I use squares that are 3-3/4 inches on a side. The paper squares need to be mounted on a stiff backing of cardboard or acrylic. The backing square should be cut slightly smaller than the paper, so that the paper extends approximately 1/8" beyond the backing on all sides. The paper can be attached to the backing square using two pieces of double-sided tape (Spray Mount or rubber cement can also be used). Great care must be taken to keep the target papers clean and to avoid scuffing them. Scuffs and blemishes will stand out in the strong projector light. This is mainly a problem for the black paper and to some extent the dark gray. I often carry extra black squares. The edge of the black paper where it has been cut is usually white and thus the projector light can reveal a thin bright line at the edge, which can damage the effect. The solution is to hold a magic marker or black Flair pen at right angles to the paper and run it along the edge, taking care not to get marks on the front of the paper. Even though the magic marker is black, it will reflect a bright sheen when spotlighted.

PROJECTOR
I prefer to use a stage spotlight, as shown in Figure 1. I use an ECT Source Four ellipsoidal spotlight. It costs about $250, uses a 575 watt bulb, but throws about the same light as other models that use 1000 watts. It is not the expensive follow-spot used to illuminate the performer, but is usually used in theater work to project decorative colored patterns. The main advantage of this spotlight is that it allows the staircase Gelb demo to be shown in a fully illuminated room.
Cheaper solutions will work, however. A slide projector will work, but the room will have to be darkened some, because the slide projector does not throw enough light. The projector should be placed near floor-level and angled up so that the light hits only the squares and not the support apparatus. An overhead projector, placed very close to the target squares also works well, as shown in Figure 2. This may allow the demo to be run with room lights on, as long as the illumination is not too bright. I prefer to show the demo in full room light because otherwise the viewers may get the impression that the illusion is somehow caused by the poor lighting conditions, which is not true.

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TARGET SUPPORT APPARATUS
I use the apparatus shown in Figure 3. It allows each target to be swung in or out of the spotlight easily. I like to mount it on some table that is approximately five feet off the floor, preferably the type of projector stand with long telescoping legs, and I mount the stage light on a short stand placed on the floor, shooting up at roughly a 45 degree angle. If an overhead projector is used for the light source, the target support apparatus should be mounted much lower, approximately at desktop height, so that the target squares are very close to the lens head that sits atop the overhead projector.
Again, simpler solutions are possible, and as long as you understand the requirements, you may come up with your own version. The means of support for the squares should not be seen within the spotlight, ideally. This is why I like to support each square (on its backing square) with a rod extending directly behind the square. The square, when in the spotlight, conceals the rod. If the rod method is used, the 5 rods should be graded in length, with the second rod about 1/8" longer than the first, and so on. This is done because it is impractical to place any two adjacent squares exactly edge to edge. It is better to overlap them slightly, so that only a single edge is visible between any two squares.
One very simple and cheap method is to stretch a taut length of black thread horizontally in front of the overhead projector. Small squares of paper (with no backing cardboard) can then be hung on the thread by folding over each paper along a line close to its top edge. The only trick then is to place the squares on the thread without your hand being seen in the spotlight. But even if your hand is seen briefly in the spotlight, this may not harm the demo. Check whether there are any bright spots, especially on the black square (in the spotlight). Often some white shows at the edge of the paper or along the fold line. Such spots can be touched up with black magic marker.

ARRANGING THE APPARATUS
Ideally the target squares should be at or somewhat above eye level for the audience. The projector light should be angled upward (downward is also an option, if the light can be mounted from the ceiling) so that it illuminates the target squares but not the support apparatus.
A crucial matter is adjusting the size and shape of the projected patch of light. It should be no larger than necessary yet easily large enough to cover all five squares in a row. With the ellipsoidal spotlight this is done with 4 blades that come in from the 4 sides. With an overhead projector this is easily accomplished by laying 4 strips of dark or opaque paper on the projector surface so as to frame the 4 boundaries of the patch. With all five target squares in viewing position, turn on the overhead projector. Bring a paper strip in from each side in turn until the occluding edge just coincides with one of the edges of the 5 square group. Then back it off some to give a little margin. Don't try to get this occluding edge too close to the edge of the squares because, even with a well-focussed projector, there will be some penumbra or chromatic abberation that may fall onto the surface of the target squares. Give yourself some leeway, for example, so that a slight accidental bump will not destroy the alignment. Tape each occluding strip down as it is brought into the correct position. Don't worry about the excess projected light that strikes a far wall or ceiling. This will not affect the demo as long as the surface is relatively far away from the apparatus.

TROUBLESHOOTING
1. The black square by itself does not appear fully white. Most likely either the projector light is not bright enough or the ambient room light is too bright. Otherwise it is possible that there is something visible within the spotlight (possibly a scratch in the paper) that has a higher reflectance than black.
2. The black square by itself appears to have a colored tint. This happens because the color of the projector light is too different from the color of the ambient light (possibly due to colored walls). A simple, all purpose solution is to lower the room lights. But the better way is to nullify most of the chromatic difference. It is usually not practical to change the color of the projected light (in small increments, that is). It is much easier to alter the color of the ambient light. For example, if the black square by itself appears too greenish, then green light needs to be added to the room. One can place a green acetate filter in front of an additional light source (such as a simple incandescent light bulb or flood light). Moving this green source closer to the display adds more green ambient light; moving it farther away dilutes the added green.