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Ray Diagrams Light Rays • Real light rays • You can’t draw every ray of light, so we use diagrams with a few special rays. Curved Mirrors Terminology center of curvature - C; the center of the “sphere” radius of curvature - r; distance from center of curvature to the mirror principal axis – a line through the center of the mirror principal focus - F; the point on the principal axis where light rays converge focal length - f; distance from the mirror to the focus f=½r Curved Mirror C F r C = center of curvature F = principal focus f = focal length r = radius f Ray Diagrams Concave (Converging) Mirrors 1. Horizontal line connecting the top of the object to the mirror; Reflects through the focus. 2. Line connecting the top of the object, the focus, and the mirror; Reflects horizontal. 3. Line connecting the top of the object, the center of curvature, and the mirror; this is also the reflected ray. C F *Image forms where rays intersect Images formed by Concave Mirrors Object Location Type of Image Beyond the center of Real, Inverted, Reduced curvature On the center of curvature Real, Inverted, Same Size Between center of Real, Inverted, Enlarged curvature and focus On the focus No Image!!! Inside focus Virtual, Upright, Enlarged *Know this Table* Images formed by Convex Mirrors See formation of convex mirror images here. Always: 1. virtual 2. upright 3. reduced 4. located behind the mirror between the vertex and focus General Image Trends (Mirrors) Real images are always: • inverted • in front of the mirror (+di) Virtual images are always: • upright • behind the mirror (-di) LENSES any transparent object having two nonparallel curved surfaces or one plane surface and one curved surface Converging Lenses - thicker in middle than in the edge These lenses converge light to a real focus Diverging Lenses - thicker at edge than in middle These lenses diverge light from a virtual focus The focus of a lens is generally NOT half-way between the center of curvature and the vertex of the lens. Ray Diagrams Converging and Diverging Lenses 1. Horizontal line connecting the top of the object to the lens; Refracts through the focus. 2. Line connecting the top of the object, the antifocus, and the lens; Refracts horizontal. 3. Line connecting the top of the object to center of the lens, refracted ray travels in the same path. *For a converging lens, the focus is behind the lens and antifocus is in front of the lens Converging Lens Ray Diagram The image characteristics depend on the object’s position with respect to one and two focal lengths (1f and 2f) away from the lens. 2f f Images formed by Converging Lenses Object Location Type of Image Beyond the center of Real, Inverted, Reduced curvature At twice the focal length Real, Inverted, Same Size Between one and two Real, Inverted, Enlarged focal lengths On the focus No Image!!! Inside focus Virtual, Upright, Enlarged *Notice: This is the same as Concave Mirrors* Images formed by Diverging Lenses Always: 1. 2. 3. 4. virtual upright reduced located between the focus and the lens (front) General Image Trends (Lenses) Real images are always: • inverted • behind the lens (+di) Virtual images are always: • upright • in front of the lens (-di) Images formed by Optical Equipment Click here for an applet that shows image formation in all types of curved mirrors and lenses.