Optometry & Visual Performance 165 Volume 14 | Issue 2 | June 2026 “I see it easier now,” Phoebe began, “but it still just looks like a bunch of numbers on a regular acuity chart.” “They are!” Professor McIver said excitedly. “But because they are derived from Weber’s Law, they have LogMAR MAR VA 0.0 1.0 20/20 0.1 1.25 20/25 0.2 1.6 20/32 0.3 2.0 20/40 0.4 2.5 20/50 0.5 3.2 20/63 0.6 4.0 20/80 0.7 5.0 20/100 0.8 6.3 20/125 0.9 8.0 20/160 1.0 10.0 20/200 1.1 12.5 20/250 1.2 16.0 20/320 1.3 20.0 20/400 tremendous power if we just notice a few things and memorize a few constants. Then we can introduce predictive analysis and make clinical work easier. Remember that every single line or step is a justnoticeable difference, or JND, so every line is a level of significance different than the one above or below. That extends not just to visual acuity, but to dioptric power and telescopic power as well. A JND is a JND is a JND.” “Wait,” E. N. said slowly, “I think I see a pattern…it seems that in the VA column, every three steps down, the denominator doubles. Oh, and same thing in the MAR column! But the numbers aren’t exact sometimes. The 32 doubles to 63 and the 63 to 125.” “Yes, E. N., correct on both counts. The first is one of the few things I want you to memorize,” Professor McIver commented. “Let’s visualize that in the columns of our chart, starting with 20/20 and dropping down three lines, or JND steps. You can see that we land on 20/40. Three more lines/steps down, and we are at 20/80, then 20/160. I want you to memorize that: on a logMAR chart, every three steps either doubles or halves the value of the denominator, depending on the direction you go. The same pattern exists in the MAR column. Here it is highlighted to make it more visible. Regarding your second observation, E.N., for those cases that are not exact, it is because of rounding extra and unneeded digits to make the concept easier to use in clinic without affecting significance of the JND.” “You may recall me saying something about being able to count to ten.” Professor McIver continued. “Well, you might also notice on the chart that not only does every three steps double or halve, but every ten LogMAR MAR VA 0 1 20/20 0.1 1.25 20/25 0.2 1.6 20/32 0.3 2.0 20/40 0.4 2.5 20/50 0.5 3.2 20/63 0.6 4.0 20/80 0.7 5.0 20/100 0.8 6.3 20/125 0.9 8.0 20/160 1.0 10.0 20/200 1.1 12.5 20/250 1.2 16.0 20/320 1.3 20.0 20/400 steps move the decimal one place. This means that if you ever have to use the logMAR scale and it goes off the available numbers on the chart, you can just move the decimal to continue. We will work on that more later, but for now, memorize that ten steps move the decimal place.” “I see what you are saying now, but what good is it in practice?” Phoebe asked. “Excellent question, and an even better segue, Phoebe,” Professor McIver began. “We know that the discovery of logarithms and the subsequent development of the slide rule led to the ability to do complex calculations easily, and an explosion in the
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