The formula

P = c x F, where c is how far the line of sight sits from the optical center in centimeters and F is the lens power in the meridian of that displacement. The canonical example: the OC sits 3 mm from the visual axis on a +4.00 D lens. c = 0.3 cm, so P = 0.3 x 4.00 = 1.2 prism diopters.

Millimeters are the trap

Bench measurements arrive in millimeters and the formula wants centimeters. Divide by 10 first. An answer ten times too large on an exam is almost always this slip.

Base direction

As a simplification, a plus lens behaves like two prisms base to base at the OC, so the base points toward the optical center. A minus lens is apex to apex: the base points away from the OC. With the OC above the visual axis, a plus lens gives base up and a minus lens base down; nasal displacement of the OC gives base in for plus and base out for minus.

The meridian-power trap

With cylinder in the Rx, the power that drives vertical prism is the power in the vertical meridian, F = S + C x sin^2(90 - axis), not the sphere. A -2.00 -1.50 x 180 lens carries -3.50 D vertically; used with a 10 mm reading drop that is the number that matters. The meridian power tool reads it directly.

Drill it on the Prentice's rule page, and see vertical imbalance for the two-eye reading problem the rule feeds.

Frequently asked questions

What does Prentice's rule assume?

A thin lens and a small decentration. It is accurate enough for dispensing decisions and exam questions; precise prism verification is still done on the instrument.

Does Prentice's rule work with cylinder?

Yes, but you must use the power in the meridian of the decentration, found with F = S + C x sin^2(theta - axis), not the sphere alone.