Concave & Convex Mirrors

Concave & Convex Mirrors is a 3D geometric-optics bench where students explore spherical reflection and image formation. A glowing object candle sits in front of a reflective mirror whose surface flips between converging (concave, positive focal length) and diverging (convex, negative focal length). Three color-coded principal rays trace from the candle flame to the mirror and reflect into space, with translucent virtual extensions behind the mirror whenever rays diverge. Live readouts compute image distance d_i from the mirror equation 1/f = 1/d_o + 1/d_i, linear magnification M = -d_i / d_o, and image classification.

• In Concave mode, place the candle beyond the center of curvature C (d_o beyond 2f) and observe the smaller, real, inverted image formed between F and C.
• Drag the candle onto C (d_o = 2f) and verify that the inverted real image has the exact same distance and size as the object (M = -1.00).
• Move the candle inside the focal point F (d_o inside f) of the concave mirror to see the rays diverge in front and converge into a magnified upright virtual image behind the mirror.
• Click the mirror dish to switch to Convex (Diverging) mode and drag the candle anywhere on the bench to confirm that a convex mirror always forms a diminished upright virtual image.
• Adjust Focal length |f| with the slider and watch the focal point F and curvature center C slide along the optical axis.

1. 1Use the mirror equation 1/f = 1/d_o + 1/d_i and magnification formula M = -d_i / d_o to locate and size spherical mirror images.
2. 2Trace the three principal rays (parallel-focal, vertex, and focal-parallel) for both concave and convex mirrors.
3. 3Explain the physical difference between a real image (light rays actually converge) and a virtual image (diverging rays appear to come from behind the mirror).
4. 4Describe how a concave mirror transitions from forming real inverted images to virtual upright images when the object crosses the focal point F.

Questions teachers ask