A Child at −9.50: Thickness, Frame Size, and Impact Resistance
A 9-year-old boy has worn −9.50 DS OU since he was six. His current glasses are CR-39 in a metal frame with a 50 mm eye size and a +2.00 front base; the edges measure about 10 mm thick, the finished pair weighs 38 g, and the lenses are badly scratched. His mother wants 'the thinnest lenses you can make, whatever the cost,' and mentions he plays youth soccer and rides his bike to school. His PD is 54 mm. The practice has 1.50, 1.60, 1.67, 1.74 and polycarbonate semi-finished blanks available, and the optician is considering a −9.50 in 1.74 in a rimless mounting to 'cut the weight.'
1. Estimate the edge thickness in 1.50 versus 1.67 for a 60 mm finished lens diameter, with a +2.00 front base and 1.5 mm centre thickness, and comment on the 1.74 plans.
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Sagitta: s = r − √(r² − (d/2)²), with r = (n − 1)/F (in mm using F in dioptres). Back surface power = −9.50 − (+2.00) = −11.50 D.
n = 1.50, 60 mm (semi-diameter 30 mm)
- Front: r = 500/2 = 250 mm → s = 250 − √(62 500 − 900) = 1.81 mm
- Back: r = 500/11.50 = 43.48 mm → s = 43.48 − √(1 890.5 − 900) = 12.01 mm
- Edge ≈ ct + back sag − front sag = 1.5 + 12.01 − 1.81 = ≈ 11.7 mm
n = 1.67, 60 mm
- Front: r = 670/2 = 335 mm → s = 335 − √(112 225 − 900) = 1.35 mm
- Back: r = 670/11.50 = 58.26 mm → s = 58.26 − √(3 394 − 900) = 8.32 mm
- Edge ≈ 1.5 + 8.32 − 1.35 = ≈ 8.5 mm
So the index change saves about 3.2 mm of edge - real, but it will not make a −9.50 look thin.
The 1.74-in-rimless plan is wrong on two counts. 1.74 is the thinnest option but is not impact-resistant and is more prone to chipping, and a rimless mounting on a child's high-minus lens puts stress on a very thin, brittle edge with no rim protection. It is the worst possible combination for a 9-year-old who plays soccer.
2. How much can the frame choice change the thickness, and what would you recommend from the frame side?
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The finished lens diameter is set largely by the frame, and thickness scales with diameter squared. Re-running the n = 1.50 numbers at a 54 mm finished diameter (semi-diameter 27 mm):
- Front: 250 − √(62 500 − 729) = 1.46 mm
- Back: 43.48 − √(1 890.5 − 729) = 9.40 mm
- Edge ≈ 1.5 + 9.40 − 1.46 = ≈ 9.4 mm - versus 11.7 mm at 60 mm, in the same material.
At 54 mm in 1.67 the estimate is ≈ 7.0 mm. In other words, dropping to a small eye size buys roughly as much as jumping two index steps, at no material cost.
Recommendation: a small-eye-size frame (A roughly 42–44 mm) that keeps the decentration low, with a PD of 54 mm meaning a frame PD near 54–58; a full rim to protect the edge; light, adjustable temples, and a bridge that actually holds so the child is not pushing the glasses up all day. Then apply the highest sensible index on top of that.
3. The mother insists on 'the thinnest, whatever the cost.' What material and mounting do you recommend, and how do you handle the impact-resistance issue?
Read the worked answer
Recommend polycarbonate (or Trivex) in a small full-rim frame. The reasoning to give the parent:
- Polycarbonate is impact-resistant by nature and is the default for a child, for sport, and for anyone at risk of eye injury. It is slightly thicker than 1.67 but the difference is a millimetre or so in a 44 mm eye size - invisible in a rim - and it will not shatter.
- Trivex is a comparable impact option with better optical clarity if the practice stocks it.
- 1.74 gives the thinnest edge but has the highest chromatic aberration, is not impact-rated, and should not be put in front of a child's eyes for daily wear or sport, and never in a rimless mount.
Handle the cost expectation honestly: show her the estimated edge thickness at 44 mm in poly versus the current 50 mm in CR-39 and let the numbers carry the argument - the frame change is doing most of the work.
Do not skip: the current CR-39 is not impact-resistant and should not go back on his face for soccer. For sport he needs ASTM F803-rated sports eyewear with polycarbonate lenses; everyday glasses, however well made, are not sports protection. Also confirm the Rx is current, consider a strap for the bike, and record the safety discussion.