P3D Why is the "face" following me???

[fj834@xxxxxxxxxxxxxxxxxxxxx (Dr. George A. Themelis)]

In the previous post I described the "hollow mask" illusion where a hollow
mask when lighted from the bottom appears to be a real face.  This is a
display called "The Living Image", available for sale from Edmund
Scientific.

Now, here is an unexpected and very intriguing property of the "Living
Image":  As you move around, the "face" seems to be following you at twice
your speed.  For example, if you look straight at the "face", it appears to
be looking straight back at you.  If you move say 15 degrees to the right
then the face appears to be turning 30 degrees to the right.  You can move
sideways or up and down and get the same effect.

To understand this, let's review the diagrams of the Reality and the (depth
reversed) illusion:


           REALITY                         Light
                                             |
                                             V
          ----------                     ----------
           \       |                    /         |
            \      |      Bright Side  /          |
  A ----->   \     |                  /           |
             /     |                  \           |
            /      |      Dark Side    \          |
        >  /       |                    \         |
      /   ----------                     ----------
  B /          ^
               |
             Light                        ILLUSION


If the observer is looking straight down at the center (A) he then sees
half bright and half dark in Reality.  This is the same with the illusion,
so the "face" (reversed object) is looking straight at you.

Now, consider what happens if the observer moves to look at an angle from
the bottom side (B).  In Reality he will see more bright and less dark. 
But if the Illusion was correct he should be seeing more dark and less
bright.  To maintain the illusion the "face" must now turn twice as much in
the same direction.

As an extreme example, consider a 45 degree viewing angle.  In reality the
observer sees only bright, no dark (because he is sighting parallel to the
dark face).  For this to happen, the object must now turn 90 degrees as
shown here:

            REALITY                     ILLUSION
                             (rotated 90 deg towards observer)
          ----------                 ----------------
           \       |                 |              |
     Bright \      |                 |              |
             \     |                 |              |
             /     |                 |              |
     Dark   /      |                  \            /
           /       |                     \       /
          ----------            Bright     \   /
                                             V
        /                                   /
       /                                   /
      /                                   /
Direction of observer           Direction of observer

(he sees only bright-no dark in both Reality and the 90 degrees rotated
illusion)

Fascinating stuff!

George Themelis

PS. This is my last posting from this account.  It closes today!  Please
use DrT-3d att.net for future correspondence.