Vertex Conversion and a Two-Millimetre PD Error in a High Myope
A 27-year-old software developer alternates between soft spherical contact lenses and glasses. Her manifest refraction through a trial frame at a 12 mm vertex distance is −12.00 DS in each eye; with −10.50 D trial lenses she reaches 20/20 and reports mild residual blur that a −0.50 D over-refraction clears. Her new glasses were ordered from the −12.00 DS refraction using monocular PDs of 34/34 taken from an old record, but pupillometry today measures 31/31. The chosen frame is a 51-19 metal with an as-worn vertex distance of 13 mm and 10° of pantoscopic tilt. She complains that the new glasses 'pull' her eyes together, that the lens edges are far thicker than she expected, and she wants to know why the contact lenses are so much weaker than the glasses.
1. Verify the contact lens power and then determine what spectacle power she actually needs at the new frame's vertex distance, given the over-refraction.
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Use the effective-power relationship, Fc = F / (1 − dF), with d in metres.
Step 1 - corneal-plane power of the refraction: Fc = −12.00 / (1 − 0.012 × (−12.00)) = −12.00 / 1.144 = −10.49 D, so −10.50 D is the correct starting lens. The calculation, not guesswork, confirms the big apparent gap between the CL and the glasses: for a −12.00 D lens, 12 mm of vertex distance is worth about 1.50 D.
Step 2 - the over-refraction is telling us the manifest was under-minused. −10.50 plus −0.50 over-refraction = −11.00 D at the corneal plane as her true ocular refraction.
Step 3 - convert that back to the spectacle plane at the new 13 mm vertex distance: F = Fc / (1 + dFc) = −11.00 / (1 + 0.013 × (−11.00)) = −11.00 / 0.857 = −12.83 D, i.e. about −12.75 D.
Judgement: the ordered −12.00 D is roughly 0.75 D under-powered for this frame. Rather than simply matching the old phoropter number, re-check the refraction at the as-worn vertex distance of the actual frame and prescribe the compensated value; explain to her that the same eye needs different numbers in a contact lens, a phoropter, and a pair of glasses that sits further out.
2. Quantify and interpret the effect of ordering 34/34 monocular PDs when her pupils measure 31/31.
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Prentice's rule: prism (Δ) = decentration (cm) × power in the meridian of the decentration. The error is 3 mm = 0.3 cm per eye in the horizontal meridian, where the power is close to −12.00 D.
P = 0.3 × 12.00 = 3.6Δ per eye, about 7.2Δ total.
Direction: the ordered PD is wider than her actual PD, so each optical centre sits temporal to the pupil and her line of sight passes through a point nasal to the optical centre. A minus lens carries its prism base away from the optical centre, so the base is nasal - base in on each eye. That is a convergent demand of roughly 7Δ she must overcome, which is exactly the 'pulling' sensation she describes and a predictable source of asthenopia and adaptation failure.
This is not a cosmetic issue: 3.6Δ per eye is far outside what a symptomatic patient should be asked to tolerate, and it is avoidable. Remake with 31/31, verified against a pupillometer measurement at the as-worn vertex and pantoscopic tilt.
3. Explain the excessive edge thickness and state what you would change on the re-order.
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Decentration drives edge thickness on a minus lens. Frame geometric centre distance is 51 + 19 = 70 mm, so half is 35 mm; her 31 mm mono PD requires about 4 mm of inward decentration per eye. The temporal edge of the finished lens therefore sits roughly 39 mm from the optical centre (its thickest point), while the nasal edge sits only about 31 mm away. With −12.00 D at 1.50 index and a 65 mm blank, that asymmetry plus the decentration cost is worth several millimetres of edge at the temporal rim - exactly the 'far thicker than expected' complaint.
Re-order strategy:
- Reduce the eye size (A ≈ 45–47 mm) and choose a frame whose geometric centre distance is close to her 62 mm PD, cutting decentration to near zero.
- Raise the index only after the frame is right; going from 1.50 to 1.67 helps, but a badly matched frame cannot be rescued by index alone.
- Keep the corrected vertex distance and PD on the order, and specify centre thickness/edge thickness targets so the lab has a stated goal.
- Counsel her that thinner and lighter lenses depend mostly on frame fit, which is why the size she chose matters more than the material.