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)
R
C
Principal axis
FV
f
Spherical Mirrors
The focal point (f) is halfway between C and V f = R / 2 R = 2f
Concave (converging) Mirror
Images will form along the focal plane from incoming rays not parallel to the
principal plane.
Inside surface of the mirror forms a “cave”
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
C < Do
Center of Curvature < Object Distance
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
F < Do < C
Focal Point < Object Distance < Center of Curvature
Real image is inverted (upside down) and larger
Do < F
Object Distance < Focal Point
Virtual image is not inverted (right side up) and larger
Ray Diagrams – Concave Mirror
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 Characteristics:Real image, Inverted, Reduced
Image Distance: approximately 17 cm
17 cm
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 Characteristics:Real image, Inverted, Magnified
Image Distance: approximately 30 cm
30 cm
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