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 Principal axis 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 Image Characteristics: Real image, Inverted, Reduced 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 Distance: approximately 30 cm Image Characteristics: Real image, Inverted, Magnified 30 cm