This simulator traces principal rays reflecting off a curved spherical mirror as you move the object and change the focal length, solving the mirror equation live to show exactly where the image forms, how large it is, and whether it is real or virtual.
• A full ray-tracing diagram with the curved mirror surface, the focal point (F), the center of curvature (C), and three principal rays traced to the resulting image. • Four live controls: mirror type (concave/convex), focal length magnitude, object distance, and object height. • Live readouts for object distance, image distance, magnification, and image type (real/virtual, upright/inverted). • Four preset scenarios: object beyond C, between F and C, inside F (magnifying-mirror mode), and a convex mirror for comparison.
1/f = 1/dₒ + 1/dᵢ relates focal length, object distance and image distance for a spherical mirror, with focal length equal to half the radius of curvature (f = R/2). Solving for image distance, dᵢ = 1/(1/f − 1/dₒ), and magnification follows as m = −dᵢ/dₒ. Unlike lenses, mirrors form real images on the SAME side as the object — the simulator's sign convention reflects that difference.
A concave mirror produces a real, inverted image when the object sits beyond the center of curvature, and a magnified, upright virtual image when the object is inside the focal point — the basis of a shaving or makeup mirror. A convex mirror, by contrast, always produces a smaller, upright, virtual image no matter where the object is, which is why convex mirrors are used for wide-field security and vehicle side mirrors — they trade image size for field of view.
1/f = 1/dₒ + 1/dᵢ, where f is focal length (half the radius of curvature), dₒ is object distance and dᵢ is image distance.
When the object is farther from the mirror than the focal length, the image is real and inverted. When the object is closer than the focal length, the reflected rays diverge — tracing them behind the mirror gives a magnified, upright virtual image.
No. A convex mirror always produces a smaller, upright, virtual image located behind the mirror surface, regardless of object distance.
Convex mirrors used for wide-field views shrink the image (magnification less than 1), which makes objects look smaller and therefore appear farther away than their true distance.