Spherical mirrors work by reflecting light rays based on their curvature, causing them to converge or diverge in predictable ways to form images.
Spherical mirrors are mirrors shaped like a section of a sphere. They come in two main types: concave (curving inward, like the inside of a spoon) and convex (curving outward, like the back of a spoon). Their ability to form images relies on the fundamental law of reflection, which states that the angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and the normal to the surface all lie in the same plane.
For spherical mirrors, the normal to the surface at any point is a line extending from that point through the mirror's center of curvature (C), which is the center of the sphere from which the mirror section is taken. Another important point is the vertex (V), the geometric center of the mirror surface, and the optical axis, a line passing through C and V.
Here's how light rays typically behave when they strike a spherical mirror, illustrating the principles:
Key Reflection Principles
- Parallel Rays: Rays traveling parallel to the optical axis of a concave mirror converge at a point called the focal point (F) after reflection. For a convex mirror, parallel rays diverge as if they originated from a focal point behind the mirror. The focal point is halfway between the vertex and the center of curvature ($F = C/2$).
- Rays Through the Focal Point: A ray passing through the focal point of a concave mirror reflects parallel to the optical axis. A ray directed towards the focal point of a convex mirror reflects parallel to the optical axis.
- Rays Through the Center of Curvature: A ray traveling along a line that goes through the center of curvature of a spherical mirror is reflected back along the same line. This is because the ray is incident along the normal to the mirror's surface at that point, resulting in an angle of incidence of zero, and thus an angle of reflection of zero.
- Rays Striking the Vertex: A ray that strikes the vertex of a spherical mirror is reflected symmetrically about the optical axis of the mirror. This means the angle of incidence with respect to the optical axis equals the angle of reflection.
Image Formation
The interaction and intersection of these reflected rays (or their extensions) determine where and how an image is formed.
- Concave Mirrors: Can form both real (where rays actually converge) and virtual (where extensions of rays appear to converge) images, depending on the object's position relative to F and C. They are often used to magnify objects or focus light, like in telescopes or makeup mirrors.
- Convex Mirrors: Always form virtual, upright, and reduced images, regardless of the object's position. They are useful for providing a wide field of view, such as in car side mirrors or store security mirrors.
By precisely controlling the shape of the mirror (its curvature) and understanding how light rays reflect according to these principles, spherical mirrors are used to manipulate light for various applications, from simple reflections to complex optical instruments.
