Spherical Mirrors
 Spherical mirror – a section of a sphere of
radius R and with a center of curvature C
R
C
Mirror
Spherical Mirrors
 The radius (R) and center of curvature (C) of the sphere
 Principal axis – a line drawn through C to the mirror
 Vertex (V) – where the principal axis intersects the mirror
 The focal point (F) and focal length (f)
Principal axis
R
f
V
F
C
Spherical Mirrors
 The focal point (f) is halfway between C and V
f=R/2
 R = 2f
Concave (converging) Mirror
Inside surface of the mirror forms a “cave”
Images will form along the focal plane
from incoming rays not parallel to the
principal plane.
Convex/Diverging Mirror
Incoming rays that are parallel to the principal axis are
reflected such that they appear to diverge from the focal point.
This gives the viewer an expanded field of view.
Ray Diagrams
 The first ray is drawn parallel to the principal axis
and is reflected through the focal point (F).
 The second ray is drawn through the center of
curvature (C), to the mirror surface, and is
reflected directly back.
 The intersection of these two rays is the position
of the image.
Ray Diagrams – Concave Mirror
Center of Curvature < Object Distance
C < Do
Real image is inverted (upside down) and smaller
Ray 1 “ focuses” in on the focal point, F, after hitting the mirror.
Ray Diagrams – Concave Mirror
Focal Point < Object Distance
< Center of Curvature
F < Do < C
Real image is inverted (upside down) and larger
Ray Diagrams – Concave Mirror
Object Distance < Focal Point
Do < F
Virtual image is not inverted (right side up) and larger
Image Characteristics
 The characteristics of the images can be
described in the following manner:
 An image may be real or virtual
 An image may be upright or inverted
 An image may be larger or smaller than the
object
Section 7.3
Image Characteristics
 Real image – an image for which the light
rays converge so that an image can be
formed on a screen

Real images form in front of the mirror where a
screen can be positioned
 Virtual image – an image for which the light
rays diverge and cannot form on a screen


Virtual images form behind or inside the mirror
where the light rays appear to converge
A virtual image results when the object is
inside the focal point
Ray Diagrams – Convex Mirror
Always has virtual image that is not inverted (right side up) and smaller
Example – Concave Mirror
 An object is placed 25 cm in front of a
concave mirror with a radius of curvature of
20 cm. Construct the ray diagram.
 Given: C = 20 cm, therefore f = 10 cm
Image Distance:
approximately 17 cm
17 cm
Image Characteristics:
Real image, Inverted, Reduced
Example – Concave Mirror
 An object is placed 15 cm in front of the
concave mirror with a radius of curvature of
20 cm. Construct the ray diagram.
 Given: C = 20 cm, therefore f = 10 cm
Image Distance:
approximately 30 cm
30 cm
Image Characteristics:
Real image, Inverted, Magnified