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.
What a learner can do afterwards
- 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
1 · Read
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.
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.
One lens equation places the image, magnification reads its flip and size, and only real images land on screens.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.