Prism by Decentration That Never Reaches the Pupil
A 47-year-old bank teller returns three days after collection with vertical double vision and a 'floor that slopes.' She was prescribed OD +4.00 −1.00 × 180 with 2Δ base down and OS +4.25 −0.75 × 175, in a 52-18 frame with monocular PDs of 31/31 and a 12 mm vertex distance. The order specified that the prism be produced by decentration 'to save weight.' On the lensmeter each lens reads its ordered back vertex power, the right lens shows 2Δ base down at the boxing centre while the left shows none, and the boxing centres of both lenses measure 31/31, matching the order. The laboratory states the job is correct because the ordered prism is present and the PD matches, and it declines to remake. She was symptom-free in her previous glasses.
1. Is the laboratory's position defensible? Work through the optics.
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No. Two measurements that look individually correct are together proof of the error.
Step 1 - power in the meridian of the prism. Base down is a vertical prism, so it depends on the vertical power. For +4.00 −1.00 × 180, the power in the 90° meridian is F = S + C·sin²θ = +4.00 + (−1.00)(sin²90°) = +4.00 − 1.00 = +3.00 D.
Step 2 - decentration needed. d = P / F = 2 / 3.00 = 0.67 cm = 6.7 mm. To put 2Δ base down at the point of wear with a plus lens, the optical centre must be 6.7 mm below that point.
Step 3 - what was actually made. The boxing centres measure 31/31, i.e. they are at the pupils. The 2Δ base down seen at the boxing centre is precisely the decentration prism created by the optical centre sitting 6.7 mm below it. So the prism exists on the lens but not at the eye: at the pupil the prism is zero.
Step 4 - the ordering error. 'Prism by decentration' and a PD specified to the pupil are mutually inconsistent: with a decentred prism design the PD must be specified to the prism reference point (the optical centre in that construction), and the blank must be large enough to allow 6.7 mm of decentration. The lab verified against the boxing centre instead of the point of wear. The patient's corrected vertical heterophoria is uncorrected again, hence the diplopia and sloping floor.
2. State the remedy and how the order should have been written.
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Remedy: remake the right lens with the 2Δ base down surfaced into the lens rather than decentred, positioned so the prism reference point coincides with her pupil at a 31 mm mono PD, and verify with the lensmeter at the point of wear - not at the boxing centre. Also re-verify the left lens (no prism, power and PD) and check that the vertical prism was intended monocularly; a unilateral vertical prism should be confirmed against the previous pair before remaking.
How the order should read:
- 'OD 2Δ base down, ground prism, prism reference point at pupil, mono PD 31 to PRP, vertex 12 mm, frame 52-18, as-worn tilt 8°.'
- If decentration is preferred for weight, the order must state the PD to the prism reference point and specify the minimum blank size, and the dispenser must accept that the boxing centre will then not sit at 31 mm.
- For a +3.00 D vertical meridian, 6.7 mm of decentration also forces a large blank and asymmetric thickness, so grinding the prism is the practical choice regardless.
Judgement: low-to-moderate power plus prescribed prism is normally surfaced, not decentred; decentration is a technique for modest prism in higher powers where the decentration stays small.
3. What verification steps would have caught this before the patient left, and what do you do for her now?
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Verification steps that would catch it:
- Check prism at the marked fitting point / point of wear, not at the boxing centre, with the lens positioned so the crosshair sits where the pupil will be. The two readings differ whenever a lens is decentred, and only one of them describes what the patient experiences.
- Confirm the prism reference point location and the mono PD to that point, and reconcile them against the frame's boxing measurements - this is where 'PD matches' and 'prism present' can both be true and still be wrong.
- Check base direction against the written order for each eye and confirm whether prism is unilateral or split.
- Check binocular balance/vertical imbalance at the dispense, and compare with the previous pair, which was symptom-free - a five-minute comparison would have flagged it.
For the patient now: acknowledge the error, provide her previous glasses as a stopgap, remake the right lens with ground prism, re-verify at the point of wear, and re-check at a short follow-up. Document the finding and the remake, and note the ordering convention in her record so the next order is unambiguous.