Converging and diverging lenses

Equipment

• Virtual converging/diverging lens on a 3D canvas
• Focal-length slider f (readout in cm)
• Incidence-angle and refractive-index sliders
• Three principal rays forming the image: through center, parallel–focal, focal–parallel

Procedure

1. Construct the image with principal rays

   In figure 1, watch three rays from the object tip: the ray through the optical center goes straight, the parallel ray refracts through the image-side focal point, and the focal ray emerges parallel. Their intersection gives the image position and orientation — read $d_i$ in the readout.

2. Verify the thin-lens formula

   Set focal length f = 10 cm and read the image position: for an object at $d_o=30$ cm the formula gives $d_i=15$ cm — compare on the readout. Bring the object closer than f: $d_i<0$, outgoing rays diverge and the image becomes virtual on the object side.

3. Change focal length and compute magnification

   Raise the focal-length slider: with $d_o>f$ the image moves farther and grows. At $d_o=30$ cm, f = 10 cm we get $m=-15/30=-0{,}5$ — a real inverted image at half size. Predict m when the object sits at $d_o=2f$ and check on the diagram.

Simulation

Experiment history

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