Plano-Convex Lens Calculator
Table of Contents
1. Plano-Convex Lens Calculator
Plano-Convex Focal Length Tool
Set one surface to infinity and solve focal length for a plano-convex lens.
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 Plano-Convex Lens Is
A plano-convex lens has one flat surface and one outward-curving convex surface. It is a common choice in imaging, illumination, collimation, and low-cost optical assemblies.
Because one face is flat, a plano-convex lens calculator only needs one real radius value instead of two curved-surface measurements.
3. Simplified Formula
If the plano side is the second surface, then R₂ = ∞ and the lens maker formula becomes:
Plano-Convex Lens Formula
1/f = (n-1)(1/R₁)
Rearranged, that means f = R₁ / (n-1). If the flat side is first instead, the infinite radius belongs to R₁ and the sign placement changes with the chosen light direction.
4. Worked Example
Given: n = 1.52, R₁ = 0.12 m, R₂ = ∞
1/f = (1.52 - 1)(1/0.12) = 0.52 × 8.333
1/f = 4.333
f = 0.231 m
5. Orientation and Design Tips
Use the curved side toward collimated light
That orientation usually minimizes spherical aberration when focusing a distant source.
Check the sign convention
The simplified formula only works cleanly when you assign the infinite radius to the correct surface for your light direction.
6. FAQ
What is a plano-convex lens calculator?
It is a focal length calculator specialized for lenses with one flat face and one convex face, so one radius is infinite.
Why is one radius infinite for a plano-convex lens?
A flat surface has zero curvature, which corresponds to an infinite radius of curvature.
Can I use the standard lens maker formula instead?
Yes. A plano-convex lens is just a special case of the lens maker formula with one radius set to infinity.
When should I use the general convex lens calculator?
Use the general convex lens calculator when both surfaces are curved or when you want to compare multiple convex lens geometries.
Related Tools & Guides
Convex Lens Calculator
Compare plano-convex and biconvex lens types in one tool.
Biconvex Lens Focal Length
See the two-curved-surface convex case.
Radius of Curvature Calculator
Solve the curved surface radius before calculating focal length.
Focal Length Calculator
Return to the general thin-lens focal length tool.
How to Calculate Focal Length
Step-by-step explanation of the calculation flow.
Materials Guide
Look up the refractive index you should use for the lens.