---
title: "Thin Lens Imaging Bench Interactive Lab | Sandbox Physics"
description: "Where does a lens form the image of an object, and when can a screen catch it? Where the light from each point of the object meets again."
canonical_url: "https://sandboxphysics.com/labs/thin-lens-imaging-bench/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/thin-lens-imaging-bench/"
last_modified: "2026-10-30"
---

Optics 021 · Where a lens puts the image

# Thin Lens Imaging Bench

**Where does a lens form the image of an object, and when can a screen catch it?** Where the light from each point of the object meets again. With a converging lens and the object beyond the focal length, that point is behind the lens, and a screen there shows a sharp, upside-down picture. Inside the focal length, or with a diverging lens, the light only seems to come from the object’s side: a virtual image, seen through the lens but never on a screen.

Slide a lit F along an optical bench. The lens puts a sharp image on the screen, or a virtual one you only see through it; find where and how large.

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

The lens is an ideal thin lens and only rays close to the axis are traced, so there is no aberration, no dispersion and no diffraction. Its default power of 10 dioptres and 25.4 mm diameter match a Thorlabs LA1509 plano-convex lens of N-BK7 glass, focal length 100 mm; other powers are ideal lenses of the same size. The iris sits at the lens and limits the cone of light. The target is an F 10 mm tall cut out of a dark mask in front of a lamp, glowing evenly. For each point of the screen the model finds the disc of the target that sends it light through the iris and adds up the lit part of that disc exactly. The picture’s brightness is that lit fraction; the iris area and the screen distance scale every point alike and are given separately as the brightness relative to the default bench. Distances are measured from the lens: the image distance is negative when the image is virtual, on the target’s side, and the magnification is negative when the image is upside down. In the scene, heights and widths are drawn 4 times larger than distances along the bench and the lens is drawn thicker than it is; every number and the screen picture use true sizes.

Physics tutorial

## Find where a lens puts the image

**Background** On an optical bench a lamp-lit target, a lens and a white screen stand on one rail. Slide the screen until the target appears on it sharp and upside down, and you have done what a projector does, and what a camera does when it focuses. The same three distances also tell why a magnifying glass works only close to the page.

**Why it matters** Knowing where the image lands and how large it is tells you where the film or sensor goes in a camera, how far a projector must stand from the wall, and why some images can never be caught on a screen at all.

Start with the essentials

- **Focus question**: Where does a lens form the image of an object, and when can a screen catch it?
- **One-sentence intuition**: Each point of the target sends a cone of light through the lens. The lens turns every ray by an amount proportional to how far from the centre it crosses, so the whole cone meets again at one point, the image of that point, a distance $s'$ behind the lens. The target’s distance $s$ and the focal length $f$ fix it. When the target is inside the focal length, the cone still spreads after the lens; it only seems to come from a point on the target’s side, a virtual image that no screen can catch.

### Core mathematical model

#### The thin-lens equation

$$
\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}=P
$$

The object distance $s$ and image distance $s'$ are measured from the lens; $f$ is positive for a converging lens and negative for a diverging one, and the power $P=1/f$ is in dioptres when $f$ is in metres. A negative $s'$ means a virtual image on the object’s side (OpenStax University Physics Vol. 3, Eq. 2.19). At $s=f$ the light leaves parallel and the image is at infinity.

#### Magnification

$$
m=\frac{h'}{h}=-\frac{s'}{s}
$$

The image height $h'$ over the object height $h$ (Eq. 2.22). A negative $m$ means upside down: every real image of a single lens is inverted, every virtual one upright. At $s=2f$ the image is the same size, $m=-1$.

#### A screen in the wrong place shows a blur

$$
b=D\left\lvert 1-\frac{L}{s'}\right\rvert,\qquad y_{L}=-\frac{L}{s}\,y
$$

The cone through an iris of diameter $D$ that meets at $s'$ is $b$ wide where the screen stands, at $L$. The patch for a target point at height $y$ is centred on the ray through the lens centre, at $y_{L}$ on the screen, so the picture lands at the same place and scale whether it is sharp or not. A smaller iris narrows every cone and keeps the picture sharper over a longer stretch of the bench.

#### Where the default lens’s 100 mm comes from

$$
f=\frac{R}{n-1}=\frac{51.5\,\mathrm{mm}}{1.5168-1}=99.7\,\mathrm{mm}
$$

A plano-convex lens with one surface of radius $R$ has this focal length. The Thorlabs LA1509 has $R=51.5\,\mathrm{mm}$ and is made of N-BK7, $n=1.5168$ at 587.6 nm, which gives 99.7 mm against the nominal 100 mm ± 1 %.

### Common difficulties

#### Covering part of the lens does not cut off part of the image

**Typical misconception** Closing the iris, or covering half the lens, removes part of the picture.

**Better mental model** Every part of the lens receives light from every point of the target and sends it to the same image point. A smaller opening makes the whole image dimmer, and sharper when the screen is out of place, but the whole F is still there.

#### A real image exists without a screen

**Typical misconception** The image is made by the screen.

**Better mental model** The light really meets at the image point and spreads again beyond it. A screen there only scatters it towards your eye; the image is there in the air, and you can see it by looking back towards the lens from beyond it.

#### A virtual image cannot be projected

**Typical misconception** Moving the screen far enough will always find the image.

**Better mental model** For a target inside the focal length, or with a diverging lens, the light leaving the lens spreads apart. No screen position collects it into a point: the image is where the light seems to come from, on the target’s side, and only an eye or a camera looking through the lens sees it.

#### Magnification is not a property of the lens alone

**Typical misconception** A lens magnifies by a fixed amount.

**Better mental model** The magnification depends on where the target is, not on the lens alone: the same 100 mm lens gives twice the size at 150 mm, the same size at 200 mm and a quarter at 500 mm.

### Run the experiment

1. 01

   #### See a sharp image

   Keep the default preset, Projector: larger and upside down.

   **What to observe:** The screen shows the F sharp, upside down and twice its size, 20 mm tall. The image distance is 300 mm and the magnification −2.

2. 02

   #### Drag the target

   Drag the lit F along the bench, away from the lens and back.

   **What to observe:** Moving the target away brings the sharp image towards the lens and makes it smaller, so the screen blurs. The purple ghost in the scene shows where the image now is; move the screen there and it is sharp again.

3. 03

   #### Put it at twice the focal length

   Load Twice the focal length: same size.

   **What to observe:** With the F at 200 mm the image forms at 200 mm, the same size and upside down: magnification −1.

4. 04

   #### Make a camera

   Load Camera: far target, small image.

   **What to observe:** With the F 500 mm away the image is at 125 mm, just beyond the focal point, and a quarter of the size. Far objects all focus close to one focal length behind the lens.

5. 05

   #### Use it as a magnifying glass

   Load Magnifying glass: virtual and upright.

   **What to observe:** At 60 mm, inside the focal length, the rays still spread after the lens. The image is virtual, 150 mm on the target’s side, upright and 2.5 times larger. The screen shows only a blur, and the curve of blur against screen distance never reaches zero.

6. 06

   #### Swap in a diverging lens

   Load Diverging lens: always virtual, smaller.

   **What to observe:** A −100 mm lens spreads the light wherever the target is. The image is virtual, upright and 0.4 times the size, 60 mm in front of the lens.

7. 07

   #### Close the iris

   Load Small iris: sharp without refocusing, then open the iris back to 25 mm.

   **What to observe:** The screen is 60 mm beyond the sharp image. With a 3 mm iris the blur is 0.6 mm and the F is readable; at 25 mm it grows to 5 mm. The small iris lets through 1.4 % as much light as the open one.

Physical conclusion

With the 100 mm lens and the F 150 mm away, the screen 300 mm behind the lens shows the F sharp, upside down and twice its size. At 200 mm, twice the focal length, the image is at 200 mm and the same size; at 500 mm it is at 125 mm and a quarter of the size. At 60 mm, inside the focal length, the image is virtual, upright and 2.5 times larger, 150 mm on the target’s side, and the screen shows only a blur. A diverging lens of −100 mm always gives a smaller upright virtual image: 0.4 times the size, 60 mm in front of the lens. Closing the iris from 25 to 3 mm shrinks the blur on a screen 60 mm too far from 5 mm to 0.6 mm, but lets through only 1.4 % as much light.

## Related experiments and articles

Continue exploring

### Images and principal rays

Move the object through the focus. Which rays still locate the image?

1. [Lab **Lenses & Refraction** Begin with the three principal rays and image orientation.](https://sandboxphysics.com/labs/lens-optics/)
2. [You are here **Thin Lens Imaging Bench** Move the object on the bench and compare real and virtual images.](https://sandboxphysics.com/labs/thin-lens-imaging-bench/)

Electron probes · Reading path

### Electron probes: reading the evidence

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Ruska: making an electron image was only the beginning**](https://sandboxphysics.com/stories/electron-evidence/ruska-electron-microscope-resolution/)
2. [Lab **Electron Optical Column** Follow the image from lens to lens](https://sandboxphysics.com/labs/electron-column/)
3. [Lab **HRTEM Phase Contrast & CTF** Compare image contrast with its transfer function](https://sandboxphysics.com/labs/hrtem-ctf/)
4. [Lab **Negative Refraction & Superlens** See a slab recover detail finer than the wavelength](https://sandboxphysics.com/labs/negative-refraction-superlens/)
5. [Lab **Parfocal Zoom Challenge** Keep a zooming image on the film](https://sandboxphysics.com/labs/parfocal-zoom-challenge/)

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)