Plano-Convex Lens Calculator

Use this plano-convex lens calculator to calculate focal length from refractive index and one curved surface radius. A plano-convex lens has one flat side, so the lens maker formula simplifies. For more generalized convex cases, use the convex lens calculator.
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Table of Contents

  1. 1. Plano-Convex Lens Calculator
  2. 2. What a Plano-Convex Lens Is
  3. 3. Simplified Formula
  4. 4. Worked Example
  5. 5. Orientation and Design Tips
  6. 6. FAQ

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.

Enter lens geometry to see the focal length.

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.

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