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Optics learning guide

Ray Tracing and Geometrical Optics Guide

Trace principal rays through mirrors and lenses, predict real and virtual images, and check the thin-lens equation in an interactive optics lab.

Open the ray-tracing lab →

Move objects and optical elements while principal rays and images update.

Start with the model

Concept overview

Geometrical optics models light as rays that travel in straight lines through uniform media and change direction at reflective or refractive boundaries. A ray diagram does more than decorate an equation: it shows where rays actually converge, where their backward extensions appear to diverge, whether an image is inverted or upright, and how image size changes with object position.

The interactive ray-tracing lab lets you move an object relative to a lens or mirror and watch principal rays update immediately. Use the diagram first to predict the image region and orientation, then use the thin-lens equation to calculate the distance. The model is most useful when the optical element is thin and the rays are paraxial; aberrations and diffraction require richer models.

Concept 1

Principal rays

For a thin converging lens, a parallel ray refracts through the far focus, a ray through the near focus exits parallel, and a central ray is approximated as undeviated.

Concept 2

Real and virtual images

A real image forms where rays physically converge and can be projected onto a screen. A virtual image forms where backward ray extensions intersect and cannot be caught on a screen at that location.

Concept 3

Signs communicate geometry

Sign conventions distinguish object side, image side, converging power, and diverging power. State the convention before substituting values instead of memorising signs without geometry.

Guided investigation

How does a converging lens image change across 2f and f?

  1. 1Select a converging lens and place the object beyond twice the focal length; record image position, size, and orientation.
  2. 2Move the object to 2f, then between 2f and f, keeping the lens unchanged.
  3. 3Move the object inside f and identify why the real rays no longer converge on the far side.
  4. 4Use the equation to calculate one image distance and compare it with the diagram.

Evidence to record

For each object region, record do, di, focal length, magnification, image type, and orientation. Include one labelled principal-ray diagram and note the modelling assumptions.

Equations and variables

1/f = 1/do + 1/di

Thin-lens or spherical-mirror relation under the chosen sign convention.

  • • f: focal length
  • • do: object distance
  • • di: image distance

m = hi/ho = -di/do

Relates linear magnification to heights and distances.

  • • m: magnification
  • • hi and ho: image and object height
  • • di and do: image and object distance

Worked example

Apply the model

An object is 30 cm from a converging thin lens with focal length 10 cm. Find the image distance and magnification.

  1. Step 1: 1/di = 1/10 - 1/30 = 2/30, so di = 15 cm.
  2. Step 2: m = -di/do = -15/30 = -0.5.

Answer: The model predicts a real image 15 cm on the far side, inverted and half the object's height. The negative magnification indicates inversion.

Misconceptions to test

Common claim

“A virtual image is imaginary and cannot be seen.”

Correction: A virtual image can be seen because rays reach the eye; it cannot be projected onto a screen at the apparent image position because rays do not physically converge there.

Common claim

“The middle of a lens creates the image.”

Correction: The entire clear aperture contributes rays to every image point. Blocking part of the lens dims the whole image rather than neatly removing the matching part.

Teacher-ready worksheet

Geometrical optics ray sheet

  1. 1.Draw three principal rays for one converging-lens case.
  2. 2.Classify four images as real or virtual and justify each.
  3. 3.Calculate image distance and magnification for one trial.
  4. 4.State the sign convention you used.
  5. 5.Name one situation where diffraction makes geometrical optics incomplete.

Print or save this page as PDF to use the investigation and worksheet offline.

Knowledge check

Check your understanding

Check image formation and the boundary between ray and wave models.

Take the wave-optics knowledge check →

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