Induced Prism & Prentice's Rule Calculator

Prentice's rule

The calculator's starting values: −4.00 D decentred 5 mm gives 4 × 5 ÷ 10 = 2.00 Δ. With the optical centre 5 mm inward (nasal) of the pupil, that prism is Base OUT (BO).

Which way the base points

A plus lens is thickest at its centre, so the base points towards the optical centre. A minus lens is thickest at the edge, so the base points away from it. Put in terms of where the optical centre has been moved from the pupil: with a plus lens the base points the same way the centre was moved; with a minus lens it points the opposite way.

Worked example: unequal lenses at the reading level

OD +4.00, OS +1.50. Reading through a bifocal or progressive, each eye looks 10 mm below its distance optical centre. The optical centres are 10 mm above the pupils, so with 10.0 mm, Up, the calculator gives OD 4.00 Δ Base UP (BU) and OS 1.50 Δ Base UP (BU).

Both bases are up, so the eyes see the difference: 4.00 − 1.50 = 2.50 Δ of vertical imbalance at the reading level. Many people fuse only 1 to 2 Δ vertically, which is why slab-off or separate reading glasses are considered for anisometropia like this.

Worked example: a frame too wide for the PD

PD 62 mm, frame 54□18, so the frame PD is 72 mm. If each optical centre sits at the frame's boxing centre, each eye looks 5 mm nasal of it: the optical centres sit 5 mm outward (temporal) of the pupils. At −6.00 D, choosing 5.0 mm and Outward, the calculator gives 3.00 Δ Base IN (BI) per eye, 6.00 Δ base in together. Decentring each optical centre 5 mm inwards removes it, if the blank is big enough: check with the minimum blank size calculator.

Astigmatic lenses

Start from the sphere, cylinder and axis as written (see how to read an eye prescription) and use the power along the direction of decentration: along 180 for horizontal decentration, along 90 for vertical. The oblique meridian calculator gives it. With an oblique cylinder the lens also produces some prism at right angles to the decentration, which a single-power calculation does not show. See the medical disclaimer.

Watch: the same calculation in the Asaan Optics desktop app

This video works a Prentice's rule example in the desktop app's calculators, not in the calculator on this page. The calculator on this page uses the same rule, for one lens power at a time.

2:30 · plays from YouTube

Video, 2 min 30 s

The Prentice rule says prism equals lens power times decentration in centimetres, and this video works one example through: a -5.00 D lens with the optical centre 4 mm in gives 2 prism dioptres, base out. It then combines 3 base in with 4 base up into a single resultant prism and runs four near vision figures: near PD, near addition, working distance and magnifier power.

Chapters

1. 00:00Six calculators
2. 00:11Prentice's rule example
3. 00:59Resultant prism
4. 01:20Near PD and near add
5. 01:53Working distance and magnifier

What the video covers

• Prentice's rule on a -5.00 D lens decentred 4 mm in: 0.4 cm x 5 D = 2 prism dioptres, base out on a minus lens
• The unit trap: the rule is in centimetres, but the decentration field asks for millimetres
• Resultant prism: 3 base in and 4 base up combine to 5 prism dioptres, base at about 53 degrees
• Near PD: a distance PD of 64 mm at 40 cm gives 60 mm, a 2 mm inset per lens
• Near addition for age 56 at 40 cm: +2.00 D as an estimate from Hofstetter's formula, to be confirmed with a subjective test
• Working distance of 50 cm as 2 dioptres, and a +12 D magnifier as 3x nominal or 4x trade magnification

Transcript

Six calculators in Asaan Optics work out prism and near vision figures for you. These tools support your judgement as an optician. They do not replace it.

In the menu, open Vision Calculators. Then choose Prentice's Rule in the list.

Prentice's rule: prism equals lens power, times decentration in centimetres. Here the optical centre has moved in, towards the nose. Select In. Enter the sphere: minus five dioptres. Take care with the unit. The rule uses centimetres, but this field asks for millimetres. For four millimetres, type four. Nought point four centimetres, times five dioptres, is two prism dioptres. On this minus lens, the base is out. Select the correct eye, and enter the cylinder and axis if the prescription has them.

Next, Resultant Prism. It combines a horizontal and a vertical prism into one. Three base in is already entered. Change the vertical prism to four, base up. The resultant is five prism dioptres, with the base at about fifty-three degrees.

Now near vision. Open Near P D. A distance P D of sixty-four millimetres, at forty centimetres, gives a near P D of sixty millimetres. Each lens is inset by two millimetres. Next, Near Addition, further down the list. Enter the age: fifty-six. At forty centimetres, the suggested add is plus two dioptres. It is an estimate, from Hofstetter's formula for age. Always confirm it with a subjective test.

Working Distance converts a distance into dioptres. Type fifty centimetres. At fifty centimetres, the demand is two dioptres. Last, Magnifier Power. A plus twelve dioptre magnifier gives three times nominal magnification, or four times in trade notation. That is six calculators for prism and near vision. Open How it works to see the formula.

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