Description
The hard part of geometric optics was never the equation, it is the ray diagram: object inside or outside twice the focal length, image upright or inverted, real or virtual. The formula gives an answer while the picture in your head refuses to match it, and a changed condition in an exam puts you back at zero. This PhET simulation's approach is that you drag the object anywhere and the principal rays and resulting image redraw immediately — where the focal points sit, how rays bend, where the image lands — which teaches more than memorizing the conclusions.
Both lenses and mirrors are covered. A lens exposes radius of curvature, index of refraction and diameter; mirrors switch between concave and convex. Change any parameter and the rays and image update at once — raise the index and the focal point pulls in; push the object through the focal point and the real image flips to virtual. What takes several redrawn diagrams on paper happens here as continuous motion. Rulers, a second light source and ray modes (marginal, principal, many, none) are all available.
From PhET Interactive Simulations at the University of Colorado Boulder. Free, HTML5, runs in a browser, and downloadable as a single HTML file for offline use.
Live ray redrawing: drag the object and the principal rays and image position follow immediately, showing the relationship between object distance, image distance and magnification as it happens.
Lenses and mirrors: converging and diverging lenses plus concave and convex mirrors, so both families of imaging behavior sit in one tool for comparison.
Adjustable optics: radius of curvature, index of refraction and diameter are continuous sliders, so focal length and image formation visibly respond to each change.
Ray display modes: marginal rays, principal rays, many rays or none, letting the view go from illustrative to uncluttered.
Focal points and virtual images: focal markers and virtual image display can be toggled, with virtual images drawn as dashed construction so the distinction stops being purely verbal.
Measurement tools: a built-in ruler and position marker allow object and image distances to be measured and checked against the equations.
Second point source: a second light point can be enabled to observe how multiple object points image separately.
Browser-based and offline-capable: HTML5 with no plugin, and a single downloadable HTML file for local use.
Free and localized: free for teaching and self-study, with the interface available in many languages.
Both lenses and mirrors are covered. A lens exposes radius of curvature, index of refraction and diameter; mirrors switch between concave and convex. Change any parameter and the rays and image update at once — raise the index and the focal point pulls in; push the object through the focal point and the real image flips to virtual. What takes several redrawn diagrams on paper happens here as continuous motion. Rulers, a second light source and ray modes (marginal, principal, many, none) are all available.
From PhET Interactive Simulations at the University of Colorado Boulder. Free, HTML5, runs in a browser, and downloadable as a single HTML file for offline use.
Features
Live ray redrawing: drag the object and the principal rays and image position follow immediately, showing the relationship between object distance, image distance and magnification as it happens.
Lenses and mirrors: converging and diverging lenses plus concave and convex mirrors, so both families of imaging behavior sit in one tool for comparison.
Adjustable optics: radius of curvature, index of refraction and diameter are continuous sliders, so focal length and image formation visibly respond to each change.
Ray display modes: marginal rays, principal rays, many rays or none, letting the view go from illustrative to uncluttered.
Focal points and virtual images: focal markers and virtual image display can be toggled, with virtual images drawn as dashed construction so the distinction stops being purely verbal.
Measurement tools: a built-in ruler and position marker allow object and image distances to be measured and checked against the equations.
Second point source: a second light point can be enabled to observe how multiple object points image separately.
Browser-based and offline-capable: HTML5 with no plugin, and a single downloadable HTML file for local use.
Free and localized: free for teaching and self-study, with the interface available in many languages.
