Optical Calculators
Quick math tools for studying and on-the-job use. Free for everyone.
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.