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Sandbox Physics

Optics · ray tracing

Lenses & Refraction

A transparent 3D lens changes from convex to concave with the focal-length sign, while three spatial principal rays refract to locate the image. Drag the object arrow or change focal length to update real and virtual images in place.

Interactive modelLenses & Refraction
Image distance0 px
Magnification0.00×
Image typereal
Orientationinverted

Physics tutorial

Lens imaging: organize all rays around the focus

BackgroundA real lens continuously refracts infinitely many rays. The thin-lens approximation concentrates refraction into one plane and summarizes curvature and refractive index with focal length.

Why it mattersThe first analysis of cameras, eyes, microscopes, and telescopes reduces to image distance, magnification, and real-versus-virtual image.

Start with the essentials

Focus question
Why does crossing the focal point suddenly move an image from a real image on one side to a virtual image on the other?
One-sentence intuition
The focus is the geometric scale for parallel-ray convergence; object position relative to it decides whether outgoing rays truly meet.

Core mathematical model

Thin-lens equation

1f=1do+1di\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}

One consistent sign convention covers converging, diverging, real, and virtual cases.

Transverse magnification

M=hiho=−didoM=\frac{h_i}{h_o}=-\frac{d_i}{d_o}

Magnitude gives size ratio while sign distinguishes upright from inverted.

Common difficulties

A virtual image is still observable

Typical misconceptionA virtual image is only a drawing aid and cannot be seen.

Better mental modelIt cannot project directly onto a screen, but eyes or another lens receive rays that appear to originate there.

Principal rays are not the only rays

Typical misconceptionThe object emits only the three rays drawn in the diagram.

Better mental modelThey are convenient representatives for locating the image; all paraxial rays obey the same imaging relation.

Run the experiment

  1. 01

    Form a reduced real image

    Place the object beyond 2F.

    What to observe: Rays converge on the far side into an inverted smaller image.
  2. 02

    Cross the focus

    Move the object slowly inside F.

    What to observe: Image distance diverges and changes sign, producing an upright virtual image.
  3. 03

    Use a diverging lens

    Set focal length negative.

    What to observe: Outgoing rays diverge and backward extensions form a reduced virtual image.