Lesson · ABO / NCLE
Lens optics
Plus and minus lenses, transposition, spherical equivalent, the optical cross, Prentice’s rule and vertex distance, worked the way the exam expects.
After this lesson you can
About 15 minutes- Read any sphero-cylinder Rx and transpose it both ways
- Find the power in any meridian with the exam’s cylinder table
- Work out induced prism and its base direction
- Compensate a strong Rx for a new vertex distance
Plus and minus lenses
A plus lens is thickest in the centre and converges light; it corrects hyperopia and presbyopia. A minus lens is thickest at the edge and diverges light; it corrects myopia. Power in diopters is the reciprocal of focal length in metres.
F = 1 / f f = 1 / F
f in metres, F in diopters
Focal length
A +4.00 D lens.
- f = 1 / 4 = 0.25 m
Answer: 25 cm (0.25 m)
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Transposition
The same lens can be written in plus-cylinder or minus-cylinder form. Contact lens work and most labs use minus cylinder, so you will transpose constantly.
- Add the cylinder to the sphere (keep the signs): that is the new sphere.
- Change the sign of the cylinder.
- Change the axis by 90° (add 90 if the axis is 90 or less, subtract 90 if it is more).
Plus cylinder to minus cylinder, and back
Rx +1.50 −2.25 × 030.
- Sphere: +1.50 + (−2.25) = −0.75
- Cylinder: −2.25 becomes +2.25
- Axis: 030 + 90 = 120
Answer: −0.75 +2.25 × 120
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Spherical equivalent
The spherical equivalent is the single sphere that puts the circle of least confusion on the retina. You use it when a small cylinder is left out, for example a spherical soft contact lens.
SE = sphere + (cylinder ÷ 2)
Spherical equivalent
Rx −3.25 −1.50 × 170.
- −3.25 + (−1.50 ÷ 2) = −4.00
Answer: −4.00 DS
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The optical cross and meridian power
A sphero-cylinder has two principal meridians 90° apart. The sphere power acts along the axis; sphere plus cylinder acts 90° away. Drawing them on an optical cross is the fastest way to see the lens.
Between the two principal meridians, the exam uses a simple table for how much of the cylinder is in effect. The table is sometimes remembered as “time is money”: the degrees off axis look like minutes past the hour, and the percentage like cents in a dollar.
| Degrees off axis | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| Cylinder in effect | 0 % | 25 % | 50 % | 75 % | 100 % |
Power in the 90° meridian
Rx +1.00 −2.00 × 060. What power acts in the 90° meridian?
- 90° is 30° off the 060 axis, so 25 % of the cylinder is in effect.
- +1.00 + (0.25 × −2.00) = +0.50
Answer: +0.50 D
Exact (sin²) optics gives +0.50; the exam wants the table value.
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Prentice’s rule and base direction
Looking through a lens anywhere except its optical centre (OC) gives prism. The amount grows with the lens power and with how far the eye is from the OC.
Δ = F × d(mm) ÷ 10
Use the power in the meridian you are moving along (the table above for a cylinder).
- Plus lens: the base is the same way the OC moved.
- Minus lens: the base is opposite to the way the OC moved.
Induced prism
A −4.00 DS lens has its OC 3 mm in (nasal) from the pupil.
- Δ = 4 × 3 ÷ 10 = 1.20 Δ
- Minus lens, OC moved in, so the base goes the opposite way: BO.
Answer: 1.20 Δ BO
Vertex distance
Moving a lens closer to or farther from the eye changes its effective power. The change grows with the square of the power, so it matters most for strong prescriptions and whenever a glasses Rx is converted to contact lenses.
Dioptric change = mm moved × F × F ÷ 1000
- Effective power: what the old lens now does at its new position. Moving it out adds plus; moving it in adds minus.
- Compensated power: what you must order so the patient gets the refracted power at the new position. It is the opposite: moving in, add plus; moving out, add minus.
Compensated power for a closer fit
Refracted +9.00 DS at 13 mm; the new frame sits at 9 mm.
- Moved in 4 mm.
- DC = 4 × 9 × 9 ÷ 1000 = 0.324 D
- Moving in, so compensate with plus: +9.00 + 0.32 = +9.32
Answer: Order about +9.32 D
Exact vergence gives +9.34. The exam uses the approximation above.
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