A convex lens converges light rays, so it can form images. With one and the same magnifying glass, the image switches between enlarged and reduced, upright and inverted, real and virtual — all depending on how far the object sits from the lens (the object distance). No other middle school optics experiment packs in this many rules.

First we'll measure the lens's focal length and "catch" a real inverted image on paper, then use the drag-and-play simulation to see all three image zones at once.

Safety first (read this section before you start)

  • Never use a magnifying glass to focus sunlight onto eyes, skin or anything flammable — it can burn skin and set paper alight. Measure the focal length with a lamp or the scene outside a window, never by pointing the lens at the sun.
  • If you use a candle as the light source, an adult must be present. Keep it well away from curtains, paper and other flammables, and blow it out as soon as you finish.

Materials and equipment

  • A magnifying glass or convex lens;
  • A sheet of white paper or white card stock to act as the "screen";
  • A light source: a distant lamp, a bright scene outside the window, or a candle (with an adult present);
  • A ruler or tape measure.

Step-by-step procedure

Step 1: measure the focal length.

  1. Aim the magnifying glass squarely at a bright, distant object (a tree outside the window, a far-off lamp).
  2. Hold the white paper behind the lens and slide it back and forth until a sharp, reduced, inverted image appears on the paper.
  3. Measure the distance from lens to paper — it is approximately the lens's focal length f (light from a distant object is nearly parallel, so the image forms close to the focal point).

Step 2: change the object distance and watch the image change. Use the candle (or lamp) as the object, line up candle, lens and paper along a straight line, and try these three cases:

  1. Object more than twice the focal length from the lens (u>2f): move the paper until you get a sharp, reduced, inverted real image;
  2. Object between one and two focal lengths away (f<u<2f): you get an enlarged, inverted real image;
  3. Object closer than one focal length (u<f): no image lands on the paper anywhere. Look through the lens instead and you see an enlarged, upright virtual image — this is how a magnifying glass is normally used.
Why the paper sometimes "catches" nothing: only a real image can land on paper (the light rays genuinely converge there). When u<f the rays leave the lens diverging and never converge, so the virtual image can only be seen by eye through the lens — the paper stays blank.
Interactive simulation: this experiment has a drag-and-play simulator in our Interactive Lab. The lab interface is currently Chinese-only — the controls are simple sliders and switches, so it is still easy to explore.

What you should observe

Suppose you measured a focal length of f = 10 cm. Recording each object distance u, image distance v and what the image looks like, one row at a time, a complete data set reads roughly:

  • u = 30 cm (>2f): v ≈ 15 cm, image inverted and reduced, sharp on the paper;
  • u = 20 cm (=2f): v ≈ 20 cm, image inverted and same size — this row is the dividing line between reduced and enlarged;
  • u = 15 cm (f<u<2f): v ≈ 30 cm, image inverted and enlarged, with the paper pushed far back;
  • u = 10 cm (=f): no matter where you put the paper, all you get is a blurry patch of light — no image forms;
  • u = 6 cm (<f): nothing lands on the paper anywhere, but looking at the object through the lens shows an upright, enlarged virtual image.

Read the u and v columns side by side and three very useful patterns emerge:

  • As u shrinks, v grows and the image grows too. That's the classroom saying "object closer, image farther and bigger." If the image grows during the experiment but you can't get it sharp, the paper probably didn't retreat along with it.
  • u and v are interchangeable. The pair u=30, v=15 and the pair u=15, v=30 are the same numbers swapped, only with the image sizes reversed. This is the reversibility of light paths.
  • A real image sits on the opposite side of the lens from the object and is inverted; a virtual image sits on the same side and is upright. "Inverted means real, upright means virtual" — a rule you can apply directly on quiz questions.
Can't get a sharp image? Check three things: 1) the candle flame, the center of the lens and the center of the paper should be at roughly the same height, or the image drifts off the paper; 2) the room may be too bright — a real image is faint, so turn off the lights or shade the setup with a paper tube; 3) the object distance may be sitting right at the focal point (u≈f), where no image forms at all — shift it a few centimeters either way and try again.

The science: three special rays and three zones

For ray diagrams there are three handy special rays: a ray parallel to the principal axis refracts through the focal point; a ray through the focal point refracts parallel to the axis; a ray through the optical center passes straight on. Where any two of them cross is where the image forms. Object distance u, image distance v and focal length f obey the lens imaging rules, and the results fit into one table:

  • u > 2f: inverted, reduced real image, located between f and 2f on the far side — a camera works in this zone;
  • u = 2f: inverted, same-size real image — the boundary between reduced and enlarged;
  • f < u < 2f: inverted, enlarged real image — projectors and slide machines use this zone;
  • u = f: the refracted rays leave parallel; no image forms;
  • u < f: upright, enlarged virtual image on the same side as the object. That's the magnifying glass.

A memory aid: the focal point divides real from virtual; twice the focal length divides reduced from enlarged. Cross f and the image flips between real and virtual; cross 2f and it flips between reduced and enlarged.

Convex lenses in everyday life

  • Cameras and phone lenses: the object is far away (u>2f), so a reduced inverted real image lands on the sensor;
  • Projectors: the slide sits between f and 2f, casting an enlarged inverted real image onto the screen;
  • Magnifying glasses: the object sits inside the focal point (u<f), giving an enlarged upright virtual image;
  • Reading glasses for farsightedness: convex lenses help converge light.

Four things students most often get wrong

  • "Cover half the lens and half the image disappears." It doesn't. Light from any single point on the object spreads across the entire lens face; blocking half only removes some of the light forming the image, so the image gets dimmer but stays complete. This question shows up on tests constantly.
  • "A virtual image doesn't exist — you can't see it." Exactly backwards: a virtual image is perfectly visible to the eye (the letters in a magnifying glass are one), it just can't be caught on paper. A real image is light genuinely converging at a spot; a virtual image is formed by the backward extensions of rays crossing. The test is whether a screen can catch it, not whether an eye can see it.
  • "The farther you hold the magnifier, the bigger the letters." True only inside the focal point. Once past one focal length, the image flips into an inverted real image. Slowly move a magnifier away from a book and you'll see the letters grow, suddenly blur, then reappear upside down. That flipping point is the focal point.
  • Measuring the focal length by pointing at the sun. A convex lens concentrates sunlight into a scorching spot that can ignite paper and burn skin, and letting it into the eye causes irreversible retinal damage. Use a tree outside the window or a distant streetlight — bright but not blinding.

Notes for teachers and parents

  • Time and grouping: two class periods on an optical bench; groups of four sharing one setup.
  • Say this before hands touch anything: candles are lit and supervised by an adult only; focusing sunlight with the magnifier is strictly forbidden.

The step most often skipped. Don't hand over the three rules up front. Have each group hunt for the position where "the image turns from reduced to enlarged" and report the object distance; pool the class data and the 2f boundary draws itself.

How to tell they truly understand. A student who can name which zone the camera, the projector and the magnifying glass each use, and explain why covering half the lens doesn't cut the image in half, has met the goal.

Take it further

  • In the simulation, drag the object slowly in from far away. Each time it crosses the 2F or F tick, pause, check the table above, and state what kind of image you have at that moment.
  • Verify "object closer, image farther and bigger" with real gear: while forming a real image, move the candle toward the lens — the paper has to retreat and the image grows.
  • Make a lens from a drop of water. Place a small water drop on plastic wrap and hold it over a newspaper: the letters are magnified. The drop's curved surface makes it a miniature convex lens — the rounder the drop (the greater its curvature), the shorter its focal length and the stronger the magnification.
  • Build a pinhole camera for comparison. Poke a small hole in one end of a box, stretch translucent paper over the other, and aim it at a bright window. It also forms an inverted real image, but unlike a lens, a pinhole needs no focusing — and its image is very dim. Comparing the two shows what the lens is really for: converging light to make the image brighter and sharper.
  • Think it over: nearsighted glasses use concave lenses, which spread light out. Why do objects look smaller when a nearsighted person peers through their own glasses?

When a student can say which zone the camera, the projector and the magnifying glass each work in and what kind of image each produces, this experiment has done its job.