What to do
The neighboring image sequence should help you to do the right thing. [It runs only once, to restart reload the page.]
What to see (or not)
The basic observation: Your right index finger should seem to vanish at its top. If this does not occur for you, check:
• Did you close the right left eye :) … etc.
• Are the arms fully stretched out?
• Thumbs nearly horizontal? [They should not overlap, a tiny gap might even help.]
Once you've discovered your blind spot, experiment a little – it's amazingly large. Also try it for the other eye; you'll notice that its position is mirrored.
[BTW: The way I here depict the hands is actually impossible, they're mirrored. When I composed the picture I started from a sign-language picture (an “L”) and never noticed the inversion until one of my daughters pointed it out to me… I simply left it in for fun.]
The image bottom right helps to understand that the center of the retina “looks” at the target. Slightly off-center (14° temporally, and 2° down) toward the nose is the “optic disk”, the place where all nerve fibres leave the eye, forming the optic nerve – at that location there is no room for photoreceptors, consequently creating the “blind spot” in the visual field.
Why do we not notice this amazingly large blind spot in everyday life? First, with both eyes open, the each eye's blind spot is filled by a seeing area of the fellow eye. But why, then, do we not notice it with one eye closed? The usual answer is “filling in” – that's just a word, the real mechanism is not well understood. But the filling-in mechanism is rather bright – it fills in a background pattern, or it fills in an object passing through the blind spot. Quite amazing, really. That's why I count it to “higher order” illusions.
The combination of outstretched arm and touching thumbs happens to end up with the correct angle (14°) for most people, since arm- and thumb lengths are correlated, nice.
At the bottom of the page I show Helmholtz' original figure – you're supposed to close left eye, fixate the cross and move towards the image until the white circle disappears. Indeed it vanishes completely at the right distance..
Helmholtz, Hermann von (1911) Handbuch der physiologischen Optik, Band II, Seite 24ff.
I learned the “finger wiggle” procedure from a talk given by Susana Martinez-Conde, thanks!
Tom Stafford has additional demos and literature background in his eBook