Plano-Convex vs. Biconvex Lens: Differences & Focal Length Formulas
Plano-convex and biconvex lenses are the two most common positive (converging) lens shapes. Both bend parallel light rays to a focus; the difference is that a plano-convex lens has only one curved surface, while a biconvex lens has two.
Key Specifications at a Glance
| Parameter | Typical Value |
|---|---|
| Substrate | N-BK7, UV fused silica |
| Diameter | 5 mm–100 mm |
| Focal length range | 15 mm–1000 mm |
| Radius tolerance | ±0.1% to ±0.5% |
| Surface accuracy | λ/4–λ/10 at 633 nm |
| Center thickness tolerance | ±0.05 mm to ±0.10 mm |
| Coating | Uncoated / single-layer MgF2 / broadband AR |
When to Use a Plano-Convex Lens
With only one curved surface, a plano-convex lens introduces less spherical aberration than a biconvex lens of the same power, which makes it the standard choice near an infinite conjugate ratio — for example, collimating light from a point source or focusing a collimated laser beam. Orient the curved side toward the collimated beam (the flat side toward the focal plane) to minimize spherical aberration.
When to Use a Biconvex Lens
Because both surfaces share the optical power, a biconvex lens can reach the same focal length with gentler curvatures than an equivalent plano-convex lens, which makes it easier to manufacture to a tight surface accuracy. Biconvex lenses perform best near a 1:1 conjugate ratio, where the object and image distances are close to equal — think relay optics or simple imaging setups rather than collimation.
Focal Length Formulas
Plano-convex lens, effective focal length (EFL)
EFL = R / (n − 1)
R is the radius of curvature of the convex surface, and n is the refractive index of the substrate at the design wavelength.
Biconvex lens, focal length (thin-lens approximation)
1/f = (n − 1) × (1/R1 − 1/R2)
R1 and R2 are the radii of curvature of the two surfaces, signed according to the standard convention (a surface convex toward the incoming light is positive).
Back focal distance (BFD), plano-convex lens
BFD ≈ EFL − (t / n)
t is the center thickness. BFD is the distance from the back surface of the lens to the focal point, and it's the number to use for mechanical positioning — not EFL.
These formulas give a close approximation. For final system design, use the EFL and BFD values listed on the actual product spec sheet rather than the calculated values.
Applications
- Laser beam expansion and focusing
- Camera and projector lens groups
- Fiber coupling and detector light collection
