A spherical mirror is a spherical cap where regular reflection of light occurs.
Types of Mirrors:
When the trajectories of light beams make small angles with the optical axis (paraxial approximation) for a spherical mirror, the following rules for their reflection applies:
Assuming that the trajectories of light beams from an object form small angles with the optical axis (paraxial approximation), in this situation the image of a convex mirror is always: virtual, upright (erected) and smaller.
Assuming that the trajectories of light beams from an object form small angles with the optical axis (paraxial approximation), you can find the different images that can produce a concave mirror in this situation (see figure).
Description of possible images in a concave mirror (see figure):To perform an algebraic analysis/study of spherical mirrors, the Gaussian reference can be adopted:
Amplification \(A\), or linear increase of an image on a spherical mirror, is given by \begin{equation} A=\frac{i}{h}=\frac{-p'}{p},\ \end{equation} where \(p\) is the object's distance to the mirror vertex, \(p'\) is the image's distance to the mirror vertex, \(h\) is the size of the object, and \(i\) is the image size. Please note: for an upright image, we have \(A\gt0\). For an inverted image, we have \(A\lt0\).
The image of an object, placed at a distance \(p\) of a focal distance \(f\) of the mirror, is formed at a distance \(p'\) of the mirror, such that \begin{equation} \frac{1}{f}=\frac{1}{p}+\frac{1}{p'}, \end{equation} where \(p\) is positive for real objects and negative to virtual objects, \(f\) is positive for the concave mirror and negative for the convex, and \(p'\) is positive for a real image and a negative for a virtual image. This equation is also valid only for paraxial approximation, i.e., for light beams which form small angles with the main axis of the mirror.