What is the equation used in manual lensometry to relate target displacement to lens power?

• A. x = f^2 Fv
• B. x = f Fv
• C. x = Fv / f
• D. x = f^2 / Fv

Answer: (A)

In manual lensometry, the displacement of the target needed to bring the image into focus depends on how strongly the test lens bends light and on the geometry set by the reference lens in the instrument. The fixed focal-length reference lens creates an imaging setup in which the target shift scales with the square of that focal length and with the vertex power of the lens under test. This yields x = f^2 Fv, meaning the target displacement x is the product of the reference focal length squared and the lens’s vertex power. DIMENSIONALLY, Fv is in diopters (1/m), f is in meters, so f^2 Fv gives meters, matching the displacement unit. If you divide x by f^2, you recover the lens power, Fv = x / f^2. The other proposed forms don’t align with this imaging geometry, where the square of the reference focal length naturally appears in the relationship.