How this calculator works
This paraxial thick-lens form includes the separation between the two refracting surfaces. Light travels from left to right: a radius is positive when its centre of curvature lies to the right of its vertex. A usual biconvex lens therefore has positive R1 and negative R2. Focal length is measured from the principal planes, rather than from a lens vertex. The index inverse requires a unique solution greater than one.
Formula
1/f = (n - 1)[1/R1 - 1/R2 + (n - 1)t/(nR1R2)]. The thickness term vanishes for t = 0.
Worked example
A thin lens with n = 1.5, R1 = +100 mm and R2 = -100 mm has power +10 D and focal length +100 mm. Doubling both radii doubles the thin-lens focal length.
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Frequently asked questions
What does a negative radius mean?
Its centre of curvature lies opposite the direction of light travel from that surface vertex.
Can I enter a plane surface?
A plane has infinite radius. Use a very large radius for an approximation; exactly infinite entries are not accepted.
Does this include chromatic aberration?
No. Enter the index at the wavelength of interest and repeat to estimate dispersion effects.