---
title: "Thin Lenses and the Lens Maker's Equation"
description: "Refraction at two curved surfaces gives a focal length set by the curvatures and the refractive index, and the thin lens equation then locates any image. Sign conventions carry most of the difficulty."
canonical: https://lightmysky.com/learn/science/thin-lenses-and-the-lens-makers-equation-mt_FXOcC5mpIM
source: https://lightmysky.com/learn/science/thin-lenses-and-the-lens-makers-equation-mt_FXOcC5mpIM.md
retrieved: 2026-09-12
---

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# Thin Lenses and the Lens Maker's Equation

Refraction at two curved surfaces gives a focal length set by the curvatures and the refractive index, and the thin lens equation then locates any image. Sign conventions carry most of the difficulty.

Subject: Science · Area: Waves, Light & Sound · Ages 19 to 20
Page: https://lightmysky.com/learn/science/thin-lenses-and-the-lens-makers-equation-mt_FXOcC5mpIM

## Ready when they can

- Uses the lens equation and a consistent sign convention to locate an image and find its magnification
- Relates focal length to surface curvature and refractive index
- Distinguishes real from virtual images and says which can be caught on a screen

## Lesson: Placing images with thin lenses

A thin converging lens bends parallel rays to one focal point, and rays through its centre sail straight on. Positions obey one over f equals one over do plus one over di, read with a single consistent sign convention. Size and flip come from m equals minus di over do: negative means inverted, and magnitude above one means enlarged.

**Example.** Put the object inside the focal length of a magnifier and the lens equation pushes di negative: the image is virtual, upright and enlarged, seen by looking through the lens. With do of 30 cm and di of 15 cm the magnification is minus 0.5, a halved inverted image. The lensmaker link sets f itself from the glass index and the two surface curvatures.

Three rays locate any image: parallel in then out through the far focus, straight through the centre, and through the near focus then out parallel. A real image lands where rays truly meet and can be caught on a screen. A virtual image is only traced back by the eye, so no screen can catch it.

*(drawing: The three trusted rays for tracing any thin image.)*

**Recap.** One lens equation places the image, magnification reads its flip and size, and only real images land on screens.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Huygens's Principle and the Laws of Reflection and Refraction](https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w)

## Opens up

- [Curved Mirrors, the Mirror Equation and Real Images](https://lightmysky.com/learn/science/curved-mirrors-the-mirror-equation-and-real-images-mt_7XqB2umthJ)
- [Magnifiers, Microscopes and Telescopes](https://lightmysky.com/learn/science/magnifiers-microscopes-and-telescopes-mt_f30rUsqYkN)