‹ Figure Out Science Optics

Converging lenses: how an image forms

Trace three rays and see why the same piece of glass turns the world into a camera, a magnifier and the human eye.

A converging lens bends light rays so they meet at a single point. This deceptively simple fact is enough to understand a camera, a microscope, a telescope and our own eye. Below, set the object distance and the focal length — the drawing recomputes the rays live.

Image distance
Magnification
Image type
Object distance15,0 cm
Focal length6,5 cm

Drag the object (or use the sliders). Bring it towards the focus F, then past it — you will see how a magnifier works.

Fig. 1 — Ray paths through a converging lens · three rays are enough to locate the image

Two rays are enough

A ray parallel to the optical axis heads for the focus on the far side after passing through the lens. A ray through the very centre keeps its direction. These two rules locate the image without any formula — it is where the rays cross again.

Key equation
1/f = 1/x + 1/y
f — focal length · x — object distance · y — image distance · magnification m = y / x

When the object is far away, the image forms just beyond the focus and is small — that is a camera. The closer the object moves to the focus, the farther and larger the image grows. Past the focus the image turns virtual and magnified — that is a magnifier.

A simplificationWe ignore aberrations, lens thickness and the colours of light. The principle of image construction stays exactly the same.

Bibliography (sample)

  1. 1 E. Hecht — "Optics", 5th ed., Pearson (2017). ISBN 978-0133977226
  2. 2 OpenStax — "University Physics, Vol. 3: Geometric Optics" (open access). openstax.org
  3. 3 R. P. Feynman — "The Feynman Lectures on Physics", Vol. I, ch. 27. caltech.edu
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