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Pantoscopic Tilt

Pantoscopic tilt refers to the frame alignment of a lens in the up-and-down position of the glasses frame.

The spherical component of the lens prescription equals the original spherical component of the lens prescription times a factor of 1 plus one-third of the sine squared of the pantoscopic tilt. The cylinderical component of the lens prescription equals the original spherical component of the lens prescription times a factor of tangent squared of the pantoscopic tilt.

Formula

{QuantityVariable[Subscript["C", "sphere"], "OpticalPower"] == QuantityVariable[Subscript["C", "original"], "OpticalPower"]*(1 + Sin[QuantityVariable["θ", "Angle"]]^2/3), QuantityVariable[Subscript["C", "cylindrical"], "OpticalPower"] == QuantityVariable[Subscript["C", "original"], "OpticalPower"]*Tan[QuantityVariable["θ", "Angle"]]^2}

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Pantoscopic Tilt"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Pantoscopic Tilt"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ResourceObject["Pantoscopic Tilt"], {QuantityVariable[ \!\(\*SubscriptBox[\("C"\), \("sphere"\)]\),"OpticalPower"] -> Quantity[2, "Diopters"], QuantityVariable[ \!\(\*SubscriptBox[\("C"\), \("cylindrical"\)]\),"OpticalPower"] -> Quantity[2, "Diopters"]}]
Out[3]=

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