Beta Ray Diagram Widget

How to read it

A real lens is two curved surfaces with glass between them. Light refracts at the front surface, travels through the thickness, and refracts again at the back, so a lens’s power is not just the sum of its surface powers. The number your lensometer reads is the back vertex power Fv — the vergence leaving the back surface for parallel light — and it is what goes on the Rx. By default you enter the front and back curves as true surface powers in diopters; switch “Curves entered as” to read them as lens-clock values instead. A Geneva lens clock reads the marked power, calibrated to 1.53 (or pick 1.523 / 1.70 for your clock), which drifts from the true power as the material index changes — the readout shows both. Grow the thickness or the index and watch Fv pull away from the simple surface sum. Tick “Show principal planes” to reveal H and H′, the planes the equivalent power is measured from.

Controls

Units:

Ray diagram

Thick lens: surface powers and back vertex powerA thick lens: front curve +10.00 D, back curve -4.00 D, center thickness 10.0 mm, index 1.50. Its back vertex power is +6.71 D (the lensometer reading). Parallel light focuses 148.9 mm in front of the back surface.VV′+10.00 D · +10.6 mk-4.00 D · -4.2 mkF′1/Fᵥ = 148.9 mmFᵥ +6.71 D · lensometer reading
A thick lens: front curve +10.00 D, back curve -4.00 D, center thickness 10.0 mm, index 1.50. Its back vertex power is +6.71 D (the lensometer reading). Parallel light focuses 148.9 mm in front of the back surface.

Readout