Concave and convex mirrors
Curved mirrors form images by reflecting light. A concave (converging) mirror curves inward and brings parallel rays together at a focal point; a convex (diverging) mirror curves outward and spreads rays apart, so its focus is virtual. The kind of image — real or virtual, enlarged or reduced, upright or inverted — depends on where the object sits relative to the focal point F and the centre of curvature C.
The mirror equation
The image position follows the mirror equation 1/f = 1/dₒ + 1/dᵢ, where f is the focal length — half the radius of curvature, f = R/2 — and dₒ, dᵢ are the object and image distances. The magnification is m = −dᵢ/dₒ. A consistent sign convention tells you whether the image is real (in front of the mirror) or virtual (behind it), and upright or inverted.
How to use the simulator
Choose the mirror type and focal length and drag the object along the axis. The tool draws the three principal rays — parallel-to-focus, through-focus, and through-centre — and marks where they meet, reporting dᵢ, the magnification and the image type in real time.
Note: the model uses the paraxial (small-angle) approximation and an ideal spherical mirror. Real mirrors show spherical aberration for wide beams, which a single focal point does not capture.
Frequently asked questions
What is the difference between a concave and a convex mirror?
A concave mirror curves inward and converges light to a focal point, so it can form real, magnified or inverted images. A convex mirror curves outward and diverges light, always forming a smaller, upright, virtual image - which is why it is used for wide-view mirrors.
What is the mirror equation?
The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance and di is the image distance. It gives the position of the image formed by a spherical mirror.
What is the focal length of a mirror?
The focal length is the distance from the mirror to its focal point, and it equals half the radius of curvature: f = R/2. It is positive for a concave mirror and negative for a convex mirror.
What is the difference between a real and a virtual image?
A real image forms where reflected rays actually meet and can be projected on a screen; a virtual image forms where the rays only appear to come from, behind the mirror, and cannot be projected.
References
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics (Wiley) — reflection, spherical mirrors and the mirror equation.
- E. Hecht, Optics (Pearson) — geometrical optics and sign conventions.
- The mirror equation 1/f = 1/do + 1/di with f = R/2 (paraxial spherical mirror).