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Induced Prism (Prentice’s Rule)

Calculate the prism induced when looking through a sphero-cylindrical lens off its optical center. Uses the effective power in the meridian of decentration and checks the ANSI Z80.1 unwanted-prism tolerance.

Induced prism
1.20Δ BI
Effective power in horizontal meridian: -3.00 D
Exceeds ANSI Z80.1 horizontal tolerance (0.67Δ)
Formula & tolerances

Power in meridian θ: Pθ = S + C · sin²(θ − axis)

Horizontal decentration → use P at θ=0° = S + C · sin²(axis)

Vertical decentration → use P at θ=90° = S + C · cos²(axis)

Δ = (decentration in cm) × |effective power|

ANSI Z80.1 unwanted-prism tolerance per lens: 0.67Δ horizontal, 0.33Δ vertical.