Converging lens simulator
Move an object along the axis of a converging (convex) lens and watch the ray diagram and the image update. The thin lens equation 1/f = 1/dₒ + 1/dᵢ gives the image distance, and the magnification M = −dᵢ/dₒ gives its size and orientation. Objects beyond f form real, inverted images; objects inside f form upright, virtual, magnified images.
What if you changed…
Move the object inside the focal length. How does the image change?
See the calculation
- 1/dᵢ = 1/10 − 1/25 = 0.06 cm⁻¹.
- Image distance = 16.67 cm. Magnification = −dᵢ/dₒ = -0.67.
- Image height = M × hₒ = -2 cm.
What this model assumes
Ideal thin converging lens and paraxial rays. A positive object distance represents a real object; negative image distance represents a virtual image.
Keep an eye on this
At the focal point, outgoing rays are parallel and there is no finite image position. Very large images may extend outside the schematic.
Understand the physics ↗Formulas used in this simulation
- Thin lens equation
- 1/f = 1/dₒ + 1/dᵢ
- Real-is-positive sign convention
- Image distance
- dᵢ = f·dₒ / (dₒ − f)
- Negative dᵢ means a virtual image
- Magnification
- M = −dᵢ/dₒ = hᵢ/hₒ
- Negative M means inverted
- Lens power
- P = 1/f
- In dioptres when f is in metres
Converging lens explorer: common questions
Wondering about the why? Start here.
How do you find the image distance for a lens?
Rearrange the thin lens equation: dᵢ = f·dₒ / (dₒ − f). With f = 10 cm and dₒ = 25 cm, dᵢ ≈ 16.7 cm.
When does a converging lens act as a magnifying glass?
When the object is closer to the lens than its focal length. The image is then virtual, upright and larger than the object, on the same side of the lens.
What happens when the object is at twice the focal length?
The image also forms at 2f on the other side. It is real, inverted and the same size as the object (M = −1).
What is a virtual image?
It appears where backward extensions of light rays meet. The rays do not actually converge there, so that image cannot be projected directly onto a screen.
What does negative magnification mean?
The image is inverted relative to the object. Its absolute value gives the ratio of image height to object height.