1. Concave/Convex Mirror Image Formation Rules 1.Parallel Rays - Light rays parallel to the principal axis are reflected through the focus of the mirror. 2. Focus Rays - Light rays through the focus of the mirror are reflected parallel to the principal axis. 3. Chief Rays – Light rays through the center of curvature of the mirror are reflected back along the same path. 4. Vertex Rays – Light rays that strike the mirror at its vertex leave at the same angle that it entered.

2. 1 2 1 2 4 4 3 3 f C Object Located Beyond f and C. object image

3. f C object image Concave Mirror Image Formation for an Object Less than f 1 2 3 4

4. Convex Mirror Image Formation f C 1 2 3 4 object image

5. Concave Mirror Image Formation Concave Mirror Beyond C Concave Mirror Between C and f Concave Mirror Image Formation Less than f

6. Lenses The focal length for a lens is dependent on both the curvature of the lens, and the lens material.

7. Convex Lens (Converging Lens) f All light rays parallel to the principal axis converge to the focal point after passing through the convex lens. Image Properties Image Type: Real or Virtual Image Orientation: Inverted or Erect Image Height (Size): Smaller, Larger, Same Image Distance: Closer, Farther, Same The image properties of a convex lens are the same as a concave mirror.

8. Concave Lens (Diverging Lens) The light rays parallel to the principal axis refract and diverge after going through the lens, such that if the refracted light rays are extended backwards, then the rays would converge at the focal point for the lens. Image Properties Image Type: Virtual Image Orientation: Erect Image Size: Smaller Image Distance: Closer The image properties of a concave lens are the same as a convex mirror. f

9. Lens Ray Image Formation Rules 1.Parallel Ray – A light ray parallel to the principal axis is refracted towards the lens focus. 2. Focal Ray - A light ray passing through the focus refracts parallel to the principal axis. 3. Chief Ray – A light passing through the center of the lens continues traveling along its original path unaffected by the lens.

10. Convex Lens Ray Diagram (Beyond f) f 2f f 1 23 3 1 2 object image

11. Convex Lens Ray Diagram (Less than f) f 2f f 1 1 object image 3 2 2

12. Concave Lens Ray Diagram f f2f object image 1 1 3 2 2 3

13. f C When do=∞, di=f, hi<<ho, real When do=C, di=C, hi=ho, real object C>do>f, do>C, hi>ho, real do from ∞ image do=f, di=∞, no image When do<f, di>do, hi>ho, virtual Image Properties Graphic (Converging Instruments)

14. Convex Mirror Image Formation f C object image do<∞, di<f, hi<ho, virtual do=∞, di=f, hi<<ho, virtual

15. Concave Lens Ray Diagram f f2f do=∞, di=f, hi<<ho, virtual do<∞, di<f, hi<ho, virtual object image