---
title: "Two Refractions inside a Thick Lens Interactive Lab | Sandbox Physics"
description: "What does the thin-lens model miss when thickness matters? The second refraction, and the glass between the two surfaces."
canonical_url: "https://sandboxphysics.com/labs/thick-lens-refraction/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/thick-lens-refraction/"
last_modified: "2026-10-29"
---

Geometrical optics · two-surface refraction

# Thick Lens Ray Tracing

**What does the thin-lens model miss when thickness matters?** The second refraction, and the glass between the two surfaces. A real ray bends at the front surface, travels through the glass and bends again at the back. Points at different depths of the object also image at different distances, so each depth needs its own bundle of rays.

Each ray hits the front sphere, refracts into the glass by Snell's law and leaves through the rear sphere. The front and rear faces of the object each send their own bundle of rays, which form images on two different planes.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

The ray paths come from tracing each ray through one surface after the other. The principal planes and effective focal length in the readouts only summarize the paraxial result.

Physics tutorial

## Thick lenses: return from one refraction plane to real interfaces

**Background** The thin-lens model ignores the distance light travels between the two curved surfaces. When the lens is thicker or more strongly curved, the two refractions happen at clearly different places, and the principal planes move away from the lens center.

**Why it matters** Camera lens groups, microscope objectives, eyes and ball lenses cannot be explained as one sudden bend. An object with depth along the axis also images each depth onto a different image plane.

Start with the essentials

- **Focus question**: How do a thicker lens and a deeper object each change where the image forms and how deep it is along the axis?
- **One-sentence intuition**: Each ray hits the front surface and refracts, travels through the glass, then hits the rear surface and refracts again; every depth in the object needs its own bundle of rays.

### Core mathematical model

#### Local Snell law

$$
n_1\sin\theta_1=n_2\sin\theta_2
$$

Angles are measured from the local surface normal at the hit point, not from the optical axis.

#### Thick-lens optical power

$$
\Phi=(n-1)\left(\frac1{R_1}-\frac1{R_2}+\frac{(n-1)t}{nR_1R_2}\right)
$$

The last term is the correction for thickness. The effective focal length is $f=1/\Phi$.

### Common difficulties

#### Real rays do not bend once at the center

**Typical misconception** Once I know the effective focal length, I can draw every real ray turning sharply at the lens center.

**Better mental model** The effective focal length only summarizes how paraxial rays enter and leave the lens. Real rays still change direction at each of the two surfaces.

#### Object depth is not object height

**Typical misconception** Drawing a taller arrow takes care of the object thickness.

**Better mental model** Depth here runs along the optical axis. The near and far faces sit at different object distances, so they form images at different distances.

### Run the experiment

1. 01

   #### Recover the thin-lens limit

   Set Lens thickness to its minimum and Object depth to zero.

   **What to observe:** The two object planes merge, the two image planes merge, and the result approaches the familiar thin lens.

2. 02

   #### Increase only lens thickness

   Keep both radii and the Glass index fixed, and increase Lens thickness.

   **What to observe:** Light travels farther inside the glass, the principal planes move and the effective focal length changes.

3. 03

   #### Give the object depth

   Increase Object depth and compare the amber and teal bundles.

   **What to observe:** The two object planes form two image planes. The image depth along the axis is generally not the same as the object depth.

Physical conclusion

The thin-lens equation is a limit of paraxial thick-lens ray tracing. Understand refraction at each surface first, then use the effective focal length as a summary.

## Related experiments and articles

Continue exploring

### When lens thickness matters

Keep the surface curvature fixed and change thickness. Does the focus stay put?

1. [You are here **Thick Lens Ray Tracing** Follow refraction at the front and rear surfaces.](https://sandboxphysics.com/labs/thick-lens-refraction/)
2. [Lab **Thick Lens Designer** Rock the lens to find its rear nodal point, and watch thickness move the focus.](https://sandboxphysics.com/labs/thick-lens-designer/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)