Thick Lens Equation Calculator

Explore thick lens optics with reliable calculations. Compare focal length, principal planes, and image formation. Export results, inspect charts, and understand every lens parameter.

Calculator Inputs

Typical crown glass is near 1.52.
Air is about 1.000. Water is about 1.333.
Use 0 for the thin-lens limit.
Enter 0 for a plano first surface.
Enter 0 for a plano second surface.
Positive distance places the object on the incoming side.
This is used for image height and magnification.
Reset

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

Surface powers: Φ1 = (nlens - nmedium) / R1, Φ2 = (nmedium - nlens) / R2
Refraction matrix: R = [[1, 0], [-Φ, 1]]
Translation matrix: T = [[1, t / nlens], [0, 1]]
System matrix: M = R2 × T × R1 = [[A, B], [C, D]]
Equivalent power: P = -C
Effective focal length: f = -nmedium / C
Image distance from back vertex: x = -nmedium(A s / nmedium + B) / (C s / nmedium + D)
Magnification: m = A + xC / nmedium

These equations follow paraxial ray-transfer optics. Distances are in millimeters, and reported optical power is converted to diopters.

How to Use This Calculator

  1. Enter the lens refractive index and the surrounding medium index.
  2. Type the front and back surface radii using the usual optical sign convention.
  3. Enter center thickness, object distance, and object height in millimeters.
  4. Press the calculate button to show the solved values above the form.
  5. 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.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.