Basic Terms Related to Image Formation by Spherical Mirror

Physics

definition

Terms related to spherical mirrors

  1. Centre of curvature (C): Centre of the sphere of which the mirror is a part.
  2. Radius of curvature (R): Radius of the sphere of which the mirror is a part.
  3. Pole (P/O): Geometric centre of the spherical surface of the mirror.
  4. Principal axis: Straight line joining the pole of the mirror to its centre of curvature.

definition

Focus, Focal length and focal plane of spherical mirrors

The plane through the focus perpendicular to the axis of a mirror or lens is called focal plane.

formula

Prove that focal length is half of radius of curvature in spherical mirrors

Consider a Concave mirror shown in the figure above.
A ray of light AB traveling parallel to the principal axis PC is incident on a concave mirror at B. After reflection, it goes through the focus F. P is the pole of the mirror. C is the center of curvature.The distance PF = focal length f. The distance PC = radius of curvature R of the mirror. BC is the normal to the mirror at the point of incidence B.
ABC = CBF (Law of reflection, i=r)
ABC = BCF (alternate angles) 
BCF = CBF
FBC is an isosceles triangle. Hence, sides BF = FC
For a small aperture of the mirror, the point B is very close to the point P,   BF = PF
PF = FC = 1/2 PC
f= 1/2 R
In a similar way, we can also prove this for convex mirror.

definition

Define focus, focal length and focal plane of spherical mirrors

Focus
Definition: 
For a concave mirror. The rays traveling parallel to the principal axis of a mirror after reflection pass through (converge at) a point F This point F is known as the principal focus of the concave mirror. It is a real point in front of a mirror.
For a convex mirror. The rays traveling parallel to the principal axis of a mirror after reflection appear to diverge from a point F on the principal axis. This point F is known as the principal focus of the convex mirror. It is a virtual point, i.e., behind the mirror.

Focal length
Definition:
The focal length (f) is the distance between the lens and the focal point.

Focal Plane:
Definition:
A vertical plane passing through the principal focus and which is perpendicular to the principal axis is called focal plane.