Vertex distance

Increasing or decreasing the vertex distance changes the optical properties of the system, by moving the focal point forward or backward, effectively changing the power of the lens relative to the eye.

Lens power in diopters is the mathematical inverse of focal length in meters.

Substituting for lens power arrives at After simplifying the final equation is found: A phoropter measurement of a patient reads −8.00 D sphere and −5.25 D cylinder with an axis of 85° for one eye (the notation for which is typically written as −8 −5.25×85).

The phoropter measurement is made at a common vertex distance of 12 mm from the eye.

The equivalent prescription at the patient's cornea (say, for a contact lens) can be calculated as follows (this example assumes a negative cylinder sign convention): Power 1 is the spherical value, and power 2 is the steeper power of the astigmatic axis: The axis value does not change with vertex distance, so the equivalent prescription for a contact lens (vertex distance, 0 mm) is −7.30 D of sphere, −4.13 D of cylinder with 85° of axis (−7.30 −4.13×85 or about −7.25 −4.25×85).