Reflection

2.6 Curved mirrors

Analyze the behaviour of light reflected from a curved mirror, after conducting experiments.

The principal points

Similar to plane mirrors, geometry is also used to analyze the behaviour of light reflecting from curved mirrors. It is therefore necessary to identify the reference points found in all curved mirrors. These principal points for curved mirrors are listed below, along with their symbols and definitions:

• Centre of curvature (C):
  The centre of curvature is a point which is equidistant from all points on the arc of the circle of which the mirror is a section;
• Radius of curvature (r):
  The radius of curvature is the distance from the centre of curvature to any point on the surface of the mirror;
• Vertex (V):
  The vertex is the geometric centre of the mirror's surface;
• Principal axis (A):
  The principal axis is a straight line passing through the centre of curvature and the vertex of the mirror.

There is another point associated with curved mirrors. Although it is not a geometric point, it is useful in predicting the behaviour of light.

• Focus (F)
  When parallel light rays are directed along the principal axis of a concave mirror, they are reflected towards one point, the focus (F). This point is sometimes referred to as the focal point.

The focus is therefore a point on the principal axis where all rays parallel to the principal axis converge. The focus of a curved mirror is always located midway between the vertex and the centre of curvature.

• Focal length (f):
  The distance from the vertex to the focus of the mirror is called the focal length (f).

The focal length is always half the radius of curvature.

Principal rays of a curved mirror
The laws of reflection
Predicting the behaviour of any ray
Parabolic mirrors
Convex mirrors