Spherical Mirrors — Core Principles

Core Principles

Spherical mirrors are curved reflecting surfaces, part of a hollow sphere. They come in two types: concave (converging, reflecting surface curves inwards) and convex (diverging, reflecting surface curves outwards).

Key terms include pole (P), center of curvature (C), radius of curvature (R), principal axis, principal focus (F), and focal length (f). For small apertures, $R = 2f$. Image formation is governed by the laws of reflection and can be analyzed using ray diagrams or the mirror formula: $1/f = 1/v + 1/u$.

Magnification, $m = h_i/h_o = -v/u$, describes image size and orientation. A consistent Cartesian sign convention is crucial for calculations: pole as origin, incident light from left, distances right of pole positive, left negative; heights above principal axis positive, below negative.

Concave mirrors can form both real (inverted, magnified/diminished/same size) and virtual (erect, magnified) images. Convex mirrors always form virtual, erect, and diminished images, providing a wide field of view.

Applications range from shaving mirrors and headlights (concave) to rearview and security mirrors (convex). Mastery requires understanding ray tracing, formula application with correct signs, and quick recall of image characteristics.

Important Differences

vs Concave Mirror vs. Convex Mirror

Aspect	This Topic	Concave Mirror vs. Convex Mirror
Reflecting Surface	Curves inwards, towards the center of the sphere.	Curves outwards, away from the center of the sphere.
Nature of Focus	Real focus (light rays actually converge at F). Focal length (f) is negative by convention.	Virtual focus (light rays appear to diverge from F). Focal length (f) is positive by convention.
Nature of Image (Real Object)	Can form both real and virtual images. Real images are inverted; virtual images are erect.	Always forms virtual, erect, and diminished images.
Magnification (m)	Can be positive (virtual image) or negative (real image). Magnitude can be >1, <1, or =1.	Always positive (virtual image) and always <1 (diminished).
Field of View	Narrow field of view.	Wide field of view.
Common Applications	Shaving mirrors, dental mirrors, headlights, solar concentrators.	Rearview mirrors in vehicles, security mirrors, street light reflectors.

Concave mirrors are converging mirrors with an inward-curving surface, capable of forming both real and virtual images depending on object position, and can magnify objects. Their focal length is considered negative. Convex mirrors are diverging mirrors with an outward-curving surface, always forming virtual, erect, and diminished images, providing a wide field of view. Their focal length is considered positive. This fundamental difference in curvature dictates their optical properties and diverse applications in daily life and technology.