Types of Mirrors
A spherical mirror is a curved reflecting surface that forms part of a sphere. Unlike flat mirrors, which produce images identical in size to the object, spherical mirrors can magnify, shrink, or even invert what you see. They appear everywhere in daily life — from the convex security mirrors in supermarkets to the concave mirrors inside torches and telescopes. Understanding how they work requires a careful look at their geometry, because the curvature of the surface is precisely what gives each mirror type its distinctive optical behaviour. There are two fundamental types of spherical mirror. A concave mirror curves inward, like the inside of a bowl or a spoon. When you hold a spoon close to your face and look at the inside surface, you see a magnified, upright image — that is a concave mirror at work. A convex mirror curves outward, like the back of the same spoon. It always produces a smaller, upright image that covers a wider field of view. This wide-angle property makes convex mirrors ideal for safety and surveillance, whereas concave mirrors are used whenever focusing or magnification is needed. Both mirror types share the same key geometric reference points: the centre of curvature C, the pole P (the midpoint of the mirror surface), the principal axis (the straight line through P and C), and the focal point F. Grasping how these points relate to the mirror's curvature is the foundation for predicting where images will form and what they will look like.
- The Centre of Curvature and Radius
- The Focal Point and Focal Length
- Sign Convention
- Ray Tracing Rules
- Properties of Images
The Centre of Curvature and Radius
Every spherical mirror is a slice of an imaginary complete sphere. The centre of that sphere is called the centre of curvature, labelled C. The distance from C to the mirror surface is the radius of curvature, R. For a concave mirror, C lies in front of the reflecting surface (on the same side as incoming light). For a convex mirror, C lies behind the reflecting surface.
The Focal Point and Focal Length
The focal point F lies exactly halfway between C and the pole P, so the focal length f = R/2. For a concave mirror, F is a real focal point: parallel rays of light actually converge there after reflection. This is why concave mirrors are called converging mirrors. For a convex mirror, parallel rays diverge after reflection, but they appear to come from a point behind the mirror — F is a virtual focal point. Convex mirrors are therefore called diverging mirrors.
Sign Convention
Physicists use the standard Cartesian sign convention: distances measured in the direction of incoming light (towards the mirror) are negative, and distances measured in the direction of the reflected light (away from the mirror, in front of it) are positive. The focal length of a concave mirror is positive (f > 0) because F is in front of the surface. The focal length of a convex mirror is negative (f < 0) because F is behind the surface. This convention keeps the mirror equation consistent across both types.
Ray Tracing Rules
Three principal rays make image construction straightforward. (1) A ray parallel to the principal axis reflects through F (concave) or appears to come from F (convex). (2) A ray directed through C reflects back along itself, because it hits the mirror surface perpendicularly. (3) A ray directed towards F reflects parallel to the principal axis. Where any two reflected rays intersect — or where their extensions behind the mirror intersect — is where the image forms. Real images form in front of the mirror; virtual images form behind it.
Properties of Images
Concave mirrors produce a wide variety of images depending on object distance: beyond C the image is real, inverted, and diminished; at C the image is real, inverted, and the same size; between C and F the image is real, inverted, and magnified; at F no image forms (rays reflect parallel); inside F the image is virtual, upright, and magnified. Convex mirrors always produce virtual, upright, and diminished images regardless of object position — a predictable, stable behaviour that makes them excellent wide-angle safety mirrors.
The Key Equation
- f — Focal length (metres (m)): Distance from the pole to the focal point. Positive for concave mirrors, negative for convex mirrors.
- v — Image distance (metres (m)): Distance from the pole to the image. Positive for real images in front of the mirror; negative for virtual images behind it.
- u — Object distance (metres (m)): Distance from the pole to the object. Taken as negative when the object is in front of the mirror (real object), following the Cartesian convention.
Worked Example
Problem. An object is placed 30 cm in front of a concave mirror with a focal length of 10 cm. Using the mirror equation, find the image distance and state whether the image is real or virtual.
Answer. The image distance is 15 cm in front of the mirror. Because v is positive, the image is real and inverted.
Origins · 1 minIbn al-Haytham (Alhazen) and how this was discovered
Ibn al-Haytham wrote the landmark Kitab al-Manazir (Book of Optics) around 1011 CE, in which he systematically analysed the reflection of light from curved mirrors — including spherical, parabolic, and cylindrical surfaces. He correctly described how concave mirrors focus light, explained the geometry of image formation, and distinguished between real and virtual images, laying the mathematical and experimental foundations that later physicists built upon. To escape persecution by the Caliph al-Hakim, Ibn al-Haytham feigned madness for over a decade — during which time he may have privately continued his scientific writing. He is considered one of the earliest practitioners of the scientific method, insisting on experimental verification long before it became standard in European science.
Related Concepts
- Image Formation by Spherical Mirrors — Once you know the two mirror types and their geometry, the natural next step is to study exactly where and how images form using ray diagrams and the mirror equation.
- Mirror Equation and Magnification — The mirror equation and magnification formula build directly on the focal length and geometry introduced for concave and convex mirrors.
- Refraction and Snell's Law — Refraction is the other fundamental interaction of light with surfaces, and understanding both reflection and refraction is essential for studying lenses and optical instruments.
- Types of Lenses — Convex and concave lenses are the refractive counterparts of concave and convex mirrors; comparing the two systems deepens understanding of converging and diverging optics.