LESSON 07 / About 28 min

Find where the image really is.

Lenses & Image Formation

Build a signed ray picture, pair object and image planes, and discover why microscope objectives depend on the rest of the optical system.

Before you begin

Light & Matter · Numerical Aperture

Try a setting, save an observation, then change one thing. The explanation checks are optional.

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Lesson outline
  1. Where does the image exist?

    A lens changes a ray’s direction. An image is where rays from one object point meet—or appear to have come from. Move the object through the focal plane and watch that distinction change.

    Real versus virtual describes ray geometry. “Virtual” does not mean invisible.

  2. Match the screen to its conjugate

    Object and image planes come as a pair. The lens equation chooses the partner plane; the camera does not choose it by being placed there.

    Changing aperture changes the out-of-plane footprint, not the paraxial conjugate distance.

  3. Two lenses make an infinity microscope

    An infinity objective sends each in-focus object point into its own parallel bundle. A tube lens turns bundle angle into image position.

    The objective encodes position as angle; the tube lens converts angle back into position.

  4. Respect the objective’s design

    A finite objective and an infinity objective aim their outgoing rays differently. Compare two ideal designs, each with its own correctly placed specimen.

    Identify the intended conjugates and the matched optical system before swapping parts.

  5. A field stop is not a pupil stop

    Two openings can have the same diameter yet control different information. One selects specimen positions; the other selects directions of light from each position.

    Ask which plane contains the stop: specimen positions or ray directions?

Model, limits & sources

All calculations are paraxial geometric optics, with ideal thin lenses and a homogeneous surrounding medium. This is not a lens prescription or a compatibility calculator.

Negative image distance denotes a virtual image on the object side; signed transverse magnification is negative for an inverted real image.

The infinity relay assumes an in-focus specimen, unlimited clear apertures, no aberrations, and a detector one tube-lens focal length behind that lens.

The stop illustration models geometric cropping and uniform-pupil light throughput. It does not calculate diffraction or an actual specimen image.

Read further

PUT THE IDEA TO WORK

Trace a selected specimen point through a complete microscope and explore focus in depth.

Continue with Follow the Light ↗

Experiment, enlarged