The six moves
| Skill | Formula | Drill |
|---|---|---|
| Transposition | S' = S + C; C' = -C; axis rotates 90 | practice |
| Prentice's rule | P = c x F in the meridian of decentration | practice |
| Vertex compensation | F' = F / (1 - d x F) | practice |
| Meridian power | F = S + C x sin^2(theta - axis) | practice |
| Minimum blank size | ED + 2 x decentration + allowance | practice |
| Vertical imbalance | Per-eye Prentice at the reading drop; difference | practice |
Supporting knowledge
Two table-reading skills ride along: the ANSI Z80.1 tolerance brackets, drilled with the tolerance checker and summarized in the reference table, and the base-direction conventions for induced prism. The spectacle magnification power factor appears occasionally and reuses the vertex denominator.
A practice plan that works
- One skill per sitting until its drill streak reaches ten with the worked steps feeling redundant.
- Switch to the mixed drill so formula selection itself gets practiced.
- Finish with timed exam runs. Time pressure is a separate skill; rehearse it before exam day, not on it.
- Keep the formula sheet printed beside you until you notice you have stopped looking at it.
Units, the recurring villain
Prentice wants centimeters, vertex wants meters, blank size stays in millimeters, and the axis lives on a 1 to 180 scale where 180 is written instead of 0. Most wrong answers on calculation questions are unit slips, which is exactly what repetition drills out.
One prescription, all six moves
The moves are easier to hold on to when they are not six unrelated formulas but six questions about the same patient. Take a right eye of -2.50 -1.50 x 180, a left eye of +1.00 sph, a 52/18 frame on a 64 mm PD with a 56 mm effective diameter, and a 12 mm vertex. Every figure in the table is computed by the same module the calculators and the drill generator use, so you can re-enter any row in the linked tool and get the identical number back.
| Move | Question about this patient | Answer | Check it |
|---|---|---|---|
| Transposition | OD -2.50 -1.50 x 180 in plus-cylinder form | -4.00 +1.50 x 090 | recompute |
| Meridian power | OD through the 90 degree meridian | -4.00 D (and -2.50 D at 180) | recompute |
| Prentice's rule | OD optical center 3 mm low | 1.20 prism diopters of unwanted vertical prism | recompute |
| Vertex compensation | OD vertical meridian -4.00 D moved from 12 mm to the cornea | -3.82 D | recompute |
| Minimum blank size | ED 56, A 52, DBL 18, patient PD 64, allowance 2 | 3 mm decentration per lens, so 64 mm blank | recompute |
| Vertical imbalance | OD -2.50 -1.50 x 180 against OS +1.00 sph at a 10 mm reading drop | 5.00 prism diopters - past the 1.50 level where slab-off is discussed | recompute |
Two things in that table are worth reading twice. The vertical meridian of the right eye is -4.00 D, not the -2.50 D sphere written on the prescription, because the cylinder axis is at 180 and so the whole cylinder lands in the vertical - and it is that vertical figure, never the sphere, that Prentice and the imbalance calculation want. And the imbalance comes out at 5.00 prism diopters from a prescription whose two spheres look only three and a half diopters apart, which is why anisometropia questions on the exam so often have a larger answer than the numbers suggest.
The axis tolerance table, which is pure recall
The one piece of this material that no formula will give you is the cylinder-axis tolerance bracket: it is a lookup, it appears on the exam, and it is short enough to simply know. The tighter the tolerance as the cylinder grows, because a given axis error misplaces more power when there is more cylinder to misplace:
| Cylinder power | Axis tolerance |
|---|---|
| 0.25 D or less | ±14 degrees |
| over 0.25 to 0.50 D | ±7 degrees |
| over 0.50 to 0.75 D | ±5 degrees |
| over 0.75 to 1.50 D | ±3 degrees |
| over 1.50 D | ±2 degrees |
For the right eye above, the -1.50 D cylinder allows 3 degrees, so an axis ground at 4 degrees off would fail while 3 degrees off would pass. Run a finished pair through the tolerance checker to see the sphere, cylinder and axis verdicts together; the full reference table carries the power brackets as well. These figures are ANSI Z80.1 as commonly published, and the standard is revised periodically - confirm the edition in force where you practice before applying a bracket to real work.