# 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.

## Image Formation by Spherical Mirror

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