Biconvex Lens Focal Length
Table of Contents
1. Biconvex Lens Calculator
Biconvex Lens Focal Length Tool
Calculate focal length for a lens with two convex surfaces.
Lens Maker Formula
1/f = (n-1)(1/R₁ - 1/R₂)
Use `∞` for a plano surface.
Convex second surfaces are usually negative.
2. What a Biconvex Lens Is
A biconvex lens has two outward-curving surfaces and is one of the most common converging lens shapes. It is used in imaging systems, magnifiers, relay optics, and many basic laboratory setups.
Because both surfaces contribute positive optical power under the usual sign convention, the focal length is positive for a properly defined biconvex lens.
3. Formula and Symmetric Shortcut
Biconvex Lens Formula
1/f = (n-1)(1/R₁ - 1/R₂)
For a symmetric biconvex lens, the magnitudes are equal: R₁ = R and R₂ = -R.
1/f = 2(n-1)/R
4. Worked Example
Given: n = 1.50, R₁ = 0.10 m, R₂ = -0.10 m
1/f = (1.50 - 1)(10 - (-10))
1/f = 0.50 × 20 = 10
f = 0.10 m
5. When to Use This Page
Use this page when
- You are specifically targeting a biconvex lens geometry.
- You want the symmetric shortcut or a worked textbook-style example.
- You already know both radii and want a direct focal length result.
Use other tools when
- You need a plano-convex calculation instead.
- You want to compare multiple convex lens shapes in one interface.
- You need thickness correction for a short, chunky element.
6. FAQ
What is the focal length formula for a biconvex lens?
Use the lens maker formula 1/f = (n-1)(1/R₁ - 1/R₂). For a symmetric biconvex lens, it simplifies to 1/f = 2(n-1)/R.
Why is R2 negative in a biconvex lens?
Under the standard Cartesian sign convention, the second convex surface has its center of curvature on the opposite side, so R₂ is negative.
Does a biconvex lens always have positive focal length?
For the normal sign convention and a real convex geometry, yes. A biconvex lens is a converging lens and therefore has positive focal length.
Should I use the thick lens calculator for biconvex lenses?
Use the thick lens calculator when the center thickness is no longer negligible relative to the radii or when you need higher design accuracy.
Related Tools & Guides
Convex Lens Calculator
Compare biconvex, plano-convex, and custom convex shapes.
Plano-Convex Lens Calculator
Switch to the one-flat-surface convex case.
Thick Lens Calculator
Add center thickness correction when needed.
Focal Length Calculator
Use the broader thin-lens focal length tool.
Radius of Curvature Calculator
Solve a missing surface radius before calculating focal length.
How to Calculate Focal Length
Step-by-step explanation of the focal length workflow.