1. Spherical Mirrors
Spherical mirror – a section of a sphere of radius R and with a center of curvature C R C
Mirror

2. 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
Principal axis f V F C

3. Spherical Mirrors The focal point (f) is halfway between C and V
f = R / 2
R = 2f

4. 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.

5. 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.

6. 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.

7. Ray Diagrams – Concave Mirror
Center of Curvature < Object Distance
C < Do
Real image is inverted (upside down) and smaller
Ray “ focuses” in on the focal point, F, after hitting the mirror.

8. Ray Diagrams – Concave Mirror
Focal Point < Object Distance < Center of Curvature
F < Do < C
Real image is inverted (upside down) and larger

9. Ray Diagrams – Concave Mirror
Object Distance < Focal Point
Do < F
Virtual image is not inverted (right side up) and larger

10. 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

11. 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

12. Ray Diagrams – Convex Mirror
Always has virtual image that is not inverted (right side up) and smaller

13. 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
Image Characteristics: Real image, Inverted, Reduced
17 cm

14. 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
Image Characteristics: Real image, Inverted, Magnified
30 cm