Calculator Inputs
Plotly Graph
The chart compares object distance with image distance and magnification using the current inputs or the built-in example.
Example Data Table
This example uses a biconvex glass lens in air and shows one solved case.
| Field | Example value |
|---|---|
| Lens refractive index | 1.52 |
| Medium refractive index | 1.00 |
| Front radius R1 (mm) | 60.00 |
| Back radius R2 (mm) | -60.00 |
| Center thickness (mm) | 8.00 |
| Object distance (mm) | 250.00 |
| Object height (mm) | 20.00 |
| Equivalent power (D) | 16.9380 |
| Effective focal length (mm) | 59.0388 |
| Image distance (mm) | 74.3448 |
| Magnification | -0.304867 |
Formula Used
These equations follow paraxial ray-transfer optics. Distances are in millimeters, and reported optical power is converted to diopters.
How to Use This Calculator
- Enter the lens refractive index and the surrounding medium index.
- Type the front and back surface radii using the usual optical sign convention.
- Enter center thickness, object distance, and object height in millimeters.
- Press the calculate button to show the solved values above the form.
- Review the chart, export the results, and compare them with the example table.
Frequently Asked Questions
1. What does the thick lens equation calculator solve?
It computes surface powers, equivalent power, effective focal length, principal plane locations, back focal distance, image distance, magnification, and image height for a thick lens.
2. Which sign convention should I use for the radii?
Use a positive radius when the surface center of curvature lies to the right of that surface. Use a negative radius when the center lies to the left.
3. Why are principal planes important?
A thick lens does not behave like a single thin plane. Principal planes shift the effective reference points, so image and focal distances are measured more accurately.
4. What does a negative image distance mean?
A negative image distance means the image forms on the same side as the object when referenced from the back vertex. That indicates a virtual image.
5. Can I model a plano-convex or plano-concave lens?
Yes. Enter 0 for a plano surface. The calculator treats that surface power as zero and still solves the full thick lens system.
6. What is the difference between effective focal length and back focal distance?
Effective focal length is measured from the principal plane. Back focal distance is measured from the back vertex. Thick lenses usually make those distances different.
7. How does the surrounding medium change the answer?
Changing the medium index alters surface power and the total matrix. A lens in water usually has lower power than the same lens in air.
8. Are these results exact for every optical system?
No. The model is paraxial, so it assumes small angles and idealized surfaces. It is excellent for first-order design, but not full aberration analysis.