Convex and Concave Mirrors - a 3D simulation

This simulation demonstrates how concave and convex mirrors form images. It uses the mirror equation, $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance. Magnification is calculated using $m=-\frac{d_i}{d_o}$.

A concave mirror can form either a real or virtual image. An object beyond the focal point produces a real, inverted image in front of the mirror. An object between the focal point and mirror produces a virtual, upright, magnified image behind the mirror.

A convex mirror always produces a virtual, upright, diminished image behind the mirror. Its wider field of view makes convex mirrors useful for vehicle mirrors, security mirrors, and observing large areas.

The coloured rays illustrate the principal-ray rules. A ray parallel to the principal axis reflects toward the focal point, a ray directed toward the focal point reflects approximately parallel to the axis, and a ray striking the vertex reflects at an equal angle. Dotted extensions indicate where diverging reflected rays appear to originate.

Use the Setup page to select the mirror type and adjust $d_o$, $f$, and the object height $h_o$. Changing $f$ also changes the mirror curvature. The object and focal point can be dragged directly along the principal axis.

Use the Rays page to display or hide individual rays and animate the object position. The Results page shows $d_i$, $m$, image orientation, and relative size. Rotate the camera to observe real images in space and virtual images appearing behind the reflective surface.