Bring it into focus

Converging lens explorer, explained.

The thin-lens equation relates focal length to object and image distance. An object outside the focal length forms a real inverted image. Inside the focal length, the outgoing rays diverge and their backward extensions meet at an upright virtual image.

The relationship to remember

1/f = 1/dₒ + 1/dᵢ · M = −dᵢ/dₒ

A worked example

With f = 10 cm and object distance 25 cm, the image distance is about 16.67 cm and magnification is −0.67. The minus sign means inverted.

Inside the default experiment

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.

When this model applies

Ideal thin converging lens and paraxial rays. A positive object distance represents a real object; negative image distance represents a virtual image.

Make a prediction. Then test it.

Move the object inside the focal length. How does the image change?

Try the interactive experiment ↗

A little question. A clearer picture.

Frequently asked questions

Wondering about the why? Start here.

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.