In this experiment a wooden board is marked with lines showing its width and length and the two diagonals from corner to corner. A notch is engraved on one of the short sides to allow the observer to hold the board up to their eyes, with the width of the board equal to the eye seperaton. Objects are then placed at various positions on the board and the observer focuses their vision on each and the results are recorded.
The effects on display here are entirely a result of the positions of the two eyes and the fact that some objects will be closer to one eye etc. Therefore to see the effects two images are rendered in POV-Ray and then stacked ontop of each other to replicate what one might see with their eyes.
al-Haytham describes 6 different combinations of the pegs on the board to observe in paragraphs 28 to 33, click the buttons below the first two images to view the results from each.
Top view of the board with points marked as in Figure III.I in paragraph 26.
Side view of the board. Three coloured pegs may be placed on the surface of the board.
Click the button below to show the results from paragraph 28:
Paragraph 28 – pegs on central width of board
Paragraph 28 considers the pegs aligned along the central width of the board.
Situation 1:
The eyes focus on the peg on point T of the board.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
Situation 2:
The eyes focus on the peg on point K of the board.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
Situation 3:
The eyes focus on the peg on point H of the board.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
In summary:
In paragraph 29 al-Haytham writes his predictions for what should be visable:
“While in this situation, the experimenter should contemplate everything on the surface of the board. He will see each of the three objects at points H, K and T single, and will also find line HKT to be one. But line EZ , which extends through the length of the board, will appear as two lines intersecting at the middle object. Similarly, when contemplating the diameters while in this situation, he will find them to be four, each of them appearing double.”
These observations are confirmed by the rendered images; one can see that the three objects do not appear as double, as well as the central red line HKT. The green line EZ does appear as two lines intersecting at the central object, and the two blue diameters appear as four distinct lines.
Click the button below to show the results from paragraph 31:
Paragraph 31 – pegs on central length of board
Paragraph 31 considers the pegs aligned along the central length of the board.
The eyes focus on the central peg at point K.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
Again, al-Haytham predicts observations that are seen in the above image:
“He will find the two objects to be four and will find them displaced from the middle, two to the right and two to the left; he will find them on two lines which are in fact the single middle line appearing double, and will find two of the four objects on one line, the other two on the other.”
Click the button below to show the results from paragraph 32:
Paragraph 32 – pegs on the diagonals
Situation 1:
The pegs are placed along one diagonal.
The eyes focus on the peg at point K.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
Situation 2:
One peg in the center and two on diagonals towards the eye.
The eyes focus on the peg at point K.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
Situation 3:
One peg in the center and two on diagonals behind the eye.
The eyes focus on the peg at point K.
View from the left and right eyes respecitvely.
Combined view from left and right eye.
In summary:
Click the button below to show the results from paragraph 33:
Paragraph 33 – peg on one edge moving out of focus
One peg is placed slightly beyond point H while the eyes focus on the peg at K. As the peg is moved further away from H along the edge, it will become doubled in the vision.
These movements give the corresponding eye views:
As it can be seen, the view of the orange peg near H begins overlapped, but as it is moved further away it becomes double.