Thick Lens Calculator

Calculator Inputs

Use the sign convention carefully. For a common biconvex lens with light traveling left to right, use R1 positive and R2 negative.

Lens refractive index

Typical crown glass is around 1.50 to 1.52.

Surrounding medium index

Use 1.00 for air, about 1.33 for water.

Center thickness (mm)

Axial thickness between the two vertex planes.

Front surface radius R1 (mm)

Positive if the center of curvature is to the right.

Rear surface radius R2 (mm)

Usually negative for a standard biconvex lens.

Aperture diameter (mm)

Used for approximate f-number and numerical aperture.

Object distance from front vertex (mm)

Enter a positive magnitude from the front vertex.

Object height (mm)

Used to estimate image height through magnification.

Example Data Table

Parameter	Example Value	Unit	Notes
Lens refractive index	1.52	—	Typical optical glass value.
Surrounding medium index	1.00	—	Air is a common surrounding medium.
Front radius R1	80	mm	Positive for the first convex surface.
Rear radius R2	-65	mm	Negative for the second convex surface.
Center thickness	8	mm	Measured along the optical axis.
Object distance	300	mm	Measured from the front vertex.
Object height	25	mm	Used for image height output.
Aperture diameter	35	mm	Used for f-number and numerical aperture.

Formula Used

F₁ = (n_lens - n_medium) / R₁

F₂ = (n_medium - n_lens) / R₂

F_eq = F₁ + F₂ - (t / n_lens)F₁F₂

EFL = n_medium / F_eq

V₁H₁ = n_medium(1 - D) / F_eq, where D = 1 - (t / n_lens)F₂

H₂V₂ = n_medium(1 - A) / F_eq, where A = 1 - (t / n_lens)F₁

BFL = EFL - H₂V₂

FFL = EFL - V₁H₁

1 / f = 1 / s + 1 / s′

m = -s′ / s

This calculator uses the thick lens form of the lensmaker relationship. Unlike thin lens approximations, it keeps the two refracting surfaces separate and includes center thickness.

The first and second principal planes shift away from the vertices as thickness increases. That shift changes front focal length, back focal length, and image location.

Distances are handled in millimeters, while reported powers are converted into inverse meters for practical optics comparison.

How to Use This Calculator

Enter the lens refractive index and the surrounding medium index.
Provide the front and rear surface radii using the stated sign convention.
Enter the center thickness of the lens in millimeters.
Fill in object distance, object height, and aperture diameter.
Click Calculate Thick Lens to view results above the form.
Review focal lengths, principal planes, image distance, magnification, and image height.
Use Download CSV for spreadsheet work and Download PDF for reporting or printing.

For reliable results, keep units consistent and verify radius signs before calculating. A wrong sign on either surface can completely change the image behavior.

FAQs

1. What makes a thick lens different from a thin lens?

A thick lens includes center thickness and separate surface powers. That means principal planes no longer sit at one simple midpoint, so focal and image distances shift from thin lens estimates.

2. Why do radius signs matter so much?

Radius signs define each surface curvature direction. Reversing a sign changes surface power, total power, and the location of principal planes, so the final optical behavior can switch dramatically.

3. What is effective focal length?

Effective focal length is the focal distance measured from the principal planes, not directly from the lens surfaces. It is the standard focal length used in paraxial thick lens analysis.

4. What is back focal length?

Back focal length is the distance from the rear vertex to the rear focal point. It is especially useful in mechanical layouts because it relates the image-side focus point to the physical lens edge.

5. Why is my image distance negative?

A negative image distance usually indicates a virtual image. This often happens when the object lies inside the effective focal length of a converging lens or when the lens behaves as a diverging system.

6. Can I use this for lenses in water or oil?

Yes. Enter the surrounding medium refractive index instead of air. The optical power changes because refraction depends on the index contrast between the lens material and the surrounding medium.

7. What does magnification tell me?

Magnification compares image height to object height. A negative value indicates an inverted real image, while a positive value indicates an upright virtual image in this paraxial sign convention.

8. Does this calculator include aberrations?

No. It is a paraxial calculator, so it models first-order imaging only. Spherical aberration, coma, astigmatism, dispersion, and manufacturing tolerances are outside this simplified calculation.