There is a concept that posits it’s not what a lens does to the patient that imparts it’s power; it’s what a patient perceives that determines how powerful the effect is through the lens. Nor are we talking purely about stimulus/response properties. This came up the other day when a friend (thank you, Linda Sanet) sent me this email:
“I was looking at your Applied Concepts book and read about the activity where a patient watches a moving Marsden ball through a minus lens and is asked to clear the letter targets on the ball while it is swinging. In school I think I was taught that the ball should appear to be moving more quickly when it passes through the minus lens. But recently I was challenged about this …” Turns out the challenge was from another good friend (thank you, Carl Hillier).
So let’s look at the Marsden ball experience in question.
This photo captures what we see through a minus lens in the monocular split pupil condition, when you position the lens edge midway below the center of your pupil. The image of the ball in the lens appears to smaller and closer to you than the original ball. But what about the relative rate of motion of the image of the ball inside or through the lens as compared to the ball outside of the lens? In the chapter on Spatial Vision that Dr. Bob Sanet and I co-authored for Drs. Penelope Suter and Lisa Harvey’s marvelous book on Vision Rehabilitation (see here), we wrote on p. 141 that the image of the ball inside the lens appears to move faster than the ball outside the lens.
To test this assertion, let’s take the Marsden Ball and put it in motion in the z-axis, where it’s moving to and fro relative to the eye, and we’ll split the pupil with a minus lens blank. See if you can judge which ball seems to have the faster relative motion – the original upper ball, or the lower, smaller ball imaged through the minus lens.
Here’s what I think — there’s very little difference between the two under these conditions. The ball through the minus lens does appear to be moving slightly faster, and that may be best explained by a motion parallax effect as noted in Figure 1 in this paper by Faubert. As long as the viewer can maintain the perception of the image through the minus lens as closer than the original image, and the two images can be viewed simultaneously, then the image which is perceived as closer will be perceived to have somewhat greater relative velocity. This matches our experiential cues in the environment. An object such as a ball thrown in the air has greater relative velocity as it approaches us.
What role does the prismatic effect of minus lenses as objects are viewed off the optical center have on your perception? The minus lens has prismatic effects that are zero at the optical center and maximal at the edges. The top of the lens has maximum base up effect and the bottom of the lens has maximum base down. Base out effects occur on both sides along the horizontal meridian. So what happens as we track the Marsden ball laterally? Essentially the dynamic movement of the object inside the virtual lens space sets up a centripetal flow.
What if we were to view a vertical object such as pencil through the lens, rather than a spherical ball? The image of the pencil inside the lens is clearly shifted inward toward the center due to maximizing the base out effects of the lens. (As an aside, it’s the same principle as hand neutralizing prism: You have an easier time judging the direction of shift with an isolated straight edge than you do with other objects of reference.) If the portion of the pencil seen outside the lens seems to be moving somewhat faster, it may be because it appears to cover a wider path in the same time frame as the compressed image inside the lens. The pencil accentuates the pendular aspect of the string, and your brain infers that a wider angle or scanpath means greater acceleration and velocity.
See what you think:
Now, what if we tape the pencil to the ball and view both the vertical and spherical effects simultaneously?
It appears to me that the spherical effect of the ball predominates over the vertical effect of the pencil, and the ball once again appears to be moving slightly faster inside the lens. You may not agree, but that’s what makes the world (or at least the ball) go round. This underscores that your perception of space and time is deeply rooted in both physical optics and psychological optics.