A curved mirror surface is usually a portion of a polished smooth spherical surface. The nature of the curved mirror depends on which of the curved surfaces is made smooth. Light will then reflect differently from these surfaces and as a result different types of images are produced.
Converging (concave) vs. Diverging (convex) Mirrors
A curved mirror can be thought of as consisting of a very large number of small plane mirrors oriented at slightly different angles. The laws of reflection always apply, regardless of the shape or smoothness of the surface.
Ray Diagrams for Converging Mirrors
Ray diagram terminology
Principal Axis
An imaginary line joining the centre of curvature (C) the principal focus (F) and the vertex (V).
Vertex (V)
The geometric centre of a curved curved mirror and the point at which the principal axis intersects the mirror.
Centre of Curvature (C)
The center of any curved reflecting surface.
Radius of Curvature (R)
A line drawn from the centre of curvature to any point on the surface of the mirror and which is also perpendicular to the surface at that point.
The length of the radius of curvature is equivalent to twice the focal length (R = 2f).
Principal Focus (F)
Rays parallel to and close to the principal axis of a concave mirror will reflect off the mirror such that they will pass through a single point called the principal focus.
Rays parallel to and close to the principal axis of a convex mirror will reflect off the mirror such that they will appear to originate from a single point called the principal focus.
Focal Length (f)
The distance between the Vertex (V) and the Principal Focus (F).
Images formed in a converging mirror
- A light ray passing parallel to the principle axis is reflected back through the focal point.
- A light ray that passes through the focal point is reflected back parallel the principle axis.
- A light ray that passes through the center of curvature reflects back along the same path.
Example of how to complete ray diagrams for converging mirrors:
An object 25 cm is located 2f from the converging mirror. What will the height of the image be?Draw a scaled ray diagram and summarize the image characteristics of each image: position, type (real or virtual), magnification (larger or smaller), attitude (upright or inverted).
Steps:
1) Select a scale to be used (1cm = 5 cm)
2) Draw a scaled diagram of the object in the correct position (arrow, top of the arrow points up)
3) Use at least two of the three special rays to locate the image(where the light rays will cross) Note: The third ray should be used as a check
4) Draw in the image, measure and convert back using the scale.