| n | R1 (mm) | R2 (mm) | t (mm) | Object (mm) | EFL (mm) | BFD (mm) | Image (mm) | m |
|---|---|---|---|---|---|---|---|---|
| 1.50 | 100 | -100 | 5 | 200 | 100.84 | 99.16 | 200.00 | -1.000 |
This example matches the default inputs in the form.
This solver uses the paraxial ray transfer matrix of a thick lens in air:
- Refraction at a surface uses a curvature term and index ratio.
- Translation models the center thickness inside the material.
- System matrix M = R2 · T(t) · R1 yields A,B,C,D.
For a lens-like system in air:
- Effective focal length: f = -1/C
- Principal planes: d1 = f(1-D), d2 = f(1-A)
- Back focal distance: BFD = f - d2
- Imaging: 1/f = 1/s + 1/s' using principal planes
- Choose a length unit and keep all values consistent.
- Enter n, R1, R2, and t.
- Use radius signs: center to the right is positive.
- Optionally enter object distance for image distance and magnification.
- Press Solve to show results under the header.
- Use Download CSV or Download PDF for documentation.
1) Why thick lenses matter in practical optics
Thin-lens formulas assume negligible thickness, but real elements are not thin. Thickness shifts the principal planes, so distance measurements must be referenced correctly.
2) Inputs that set optical power
Power depends on refractive index n, surface radii R1 and R2, and center thickness t. Many common glasses fall near n = 1.45 to 1.80.
3) Interpreting radius signs and plano surfaces
A radius is positive when its center of curvature is to the right of the surface. For left-to-right light in a biconvex lens, R1 > 0 and R2 < 0 is a typical pairing. Enter 0 to model a plano surface.
4) Matrix model used for the calculation
The solver uses a paraxial ray-transfer matrix composed of two refractions and one internal translation. The final matrix elements A,B,C,D describe how height and angle propagate. In air, the effective focal length is computed using f = -1/C.
5) Principal planes and distances you can measure
Thick lenses have two principal planes, H1 and H2, that can lie inside the element. The back focal distance (BFD) is measured from the second surface and matters for mounts and sensor spacing.
6) Image position and magnification
If you provide object distance, the solver applies Gaussian imaging using distances referenced to the principal planes. It returns image distance from the second surface and magnification m.
7) Typical numeric behavior for quick validation
A biconvex lens with radii near ±100 mm and n=1.50 often produces an EFL close to 100 mm. Large deviations usually come from unit mismatch or incorrect radius signs.
8) Reporting data in an engineering workflow
Record the unit system, measured thickness, and index at the intended wavelength. Use CSV for lab notebooks and PDF for clean shareable summaries.
1) What does a negative image distance mean?
It indicates a virtual image relative to the second surface, located on the object side. Virtual images cannot be projected onto a screen without additional optics.
2) Can I enter a plano surface?
Yes. Enter 0 for the radius to represent an effectively infinite radius. The solver treats it as flat while still applying the index change at the interface.
3) Why does thickness change the answer?
Thickness moves the principal planes and changes focal distances measured from the physical surfaces. Even when EFL shifts modestly, BFD and imaging distances can shift enough to matter in hardware.
4) Which sign convention should I use for radii?
Use the convention shown on the page: positive when the curvature center lies to the right of the surface. For a common biconvex lens with left-to-right light, R1 is positive and R2 is negative.
5) What range of refractive index is reasonable?
Many optical glasses are between about 1.45 and 1.80. If you enter values near 1.00, the element behaves like air and power drops. Very high values can exaggerate sensitivity to sign and units.
6) What does optical power represent?
Optical power is the inverse of focal length in meters, with sign included. Higher magnitude means stronger focusing. It is convenient for comparing lenses and estimating system behavior during early design.
7) Why do my results look unrealistic?
Check units first, then verify radius signs. A wrong sign can turn a converging lens into a diverging one. Also ensure thickness is not accidentally entered in different units than the radii.