This board supports two models only. The first is the wave equation v = fλ, where you choose which quantity to find. The second is the thin converging lens equation, which gives image distance, whether the image is real or virtual, upright or inverted, and the magnification.
A conceptual wave animation sits under the wave model to show what wavelength and amplitude look like. It is not drawn to scale.
How do I use it?
- Choose a model: the wave equation or the thin converging lens.
- For waves, choose what to find (speed, frequency or wavelength). The two other boxes are the known values, and both must be positive.
- For the lens, enter the focal length f and object distance u in cm, both positive. Add an object height in cm if you want the image height.
- Press Calculate. Reset restores the starting example.
- For waves, use Pause animation or Play animation as you like.
Example walk-through
The wave model opens on “find speed” with f = 50 Hz and λ = 2 m. Then v = 50 × 2 = 100 m/s, and the period is T = 1 / 50 = 0.02 s. Change “Find” to frequency, enter v = 340 and λ = 0.5, and you get f = 340 / 0.5 = 680 Hz.
Switch to the lens with f = 10 cm and u = 30 cm. The equation 1/v = 1/10 - 1/30 gives v = 15 cm.
The magnification is 15 / 30 = 0.5, so the image is real, inverted and smaller than the object. With an object height of 4 cm, the image height is -2 cm, and the minus sign means inverted.
Now move the object closer: u = 5 cm with f = 10 cm. The image distance is negative, so the image is virtual, 10 cm from the lens on the object’s side.
The magnification is 2, so it is upright and larger, and a 4 cm object gives an 8 cm image. Set u = 10 cm to see the case where no image forms.
How do I read the result?
- Wave result: shows v, f and λ together, with the period T = 1 / f.
- Lens equation line: shows the substitution, so you can see each step.
- Real or virtual: a positive image distance is real (opposite side), a negative one is virtual (same side).
- Size and orientation: real images here are inverted, virtual images are upright, and the magnification tells you larger or smaller.
What are the limits?
The board covers only the wave equation and the paraxial thin converging lens. It does not calculate diverging lenses, thick lenses or other ray rules, and it gives no experiment instructions.
The wave animation is a concept picture. Amplitude and wavelength in it are not tied to your numbers, so use the result text for values.
Which lessons explain the output?
Start with connecting wavelength, frequency and speed and reading amplitude without doubling it. For lenses, see drawing a simple lens image and real and virtual image construction.
Mixed questions are in the wave behaviour practice set and the light and imaging practice set. More aids are on the tools page.
When the ray diagram and the equation give different answers in your work, our team can compare them with you. See online one-to-one Physics tuition for how that works.