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Mirrors & Lenses

Mirrors & Lenses. Chapter 23. Chapter 23 Learning Goals. Understand image formation by plane or spherical mirrors Understand image formation by converging or diverging lenses. Understand Image Formation by Plane or Spherical Mirrors.

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Mirrors & Lenses

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  1. Mirrors & Lenses Chapter 23

  2. Chapter 23 Learning Goals • Understand image formation by plane or spherical mirrors • Understand image formation by converging or diverging lenses

  3. Understand Image Formation by Plane or Spherical Mirrors • Relate the focal point of a spherical mirror to its center of curvature • Locate the image of a real object and determine if the image is: • Real or virtual • Upright or inverted • Enlarged or Reduced

  4. Flat Mirrors • Use a picture to define the following • image and object ( I & O) • image & object distance ( q & p ) • image & object height ( h’ & h ) • real image • virtual image

  5. Flat Mirrors

  6. Summary of Flat Mirrors • The image is as far behind the mirror as the object is in front of the mirror • The image is unmagnified, virtual, & upright

  7. Spherical Mirrors • Two types of spherical mirrors • Concave Mirror • Convex Mirror

  8. Spherical Mirrors • Use a picture to define the following for a concave mirror and convex mirror • principal axis • center of curvature ( C ) • radius of curvature ( R ) • image point and object ( I & O) • image & object distance ( q & p ) • image & object height ( h’ & h )

  9. Focal Length Shown by Parallel Rays

  10. Spherical Mirrors • When the object is very far from the mirror • The image point is halfway between the center of curvature and the center of the mirror • The image point will be called the focal point • The image distance will be called the focal length

  11. Spherical Mirrors

  12. Ray Diagram for Concave Mirror, p > R

  13. Ray Diagram for a Concave Mirror, p < f

  14. Ray Diagram for a Convex Mirror

  15. Spherical Mirrors • Magnification Equation M = image height = h’ = - q object height h p

  16. Spherical Mirrors • Mirror Equation 1 + 1 = 2 pq R • Mirror Equation in terms of focal length 1 + 1 = 1 pqf

  17. Front, or real, side R is positive p & q positive incident light ------------- reflected light Back, or virtual, side p & q negative R is negative No light Ray Diagrams (Mirrors)

  18. Sign Convention for Mirrors

  19. Ray Diagrams • Steps for Drawing ray diagrams • Ray 1 is parallel to the principal axis & is reflected through the focal point, F • Ray 2 is drawn through the focal point, & reflected parallel to the principal axis. • Ray 3 is drawn through the center of curvature, C, and is reflected back on itself.

  20. Ray Diagrams • The intersection of any two of these rays at a point locates the image

  21. Summary of Thin Lenses

  22. Spherical Abberation • Rays are generally assumed to make small angles with the mirror • When the rays make large angles, they may converge to points other than the image point • This results in a blurred image

  23. Understand image formation by converging or diverging lenses • Know what factors affect the focal length of lenses • Determine by ray tracing: • Location of the image of a real object: • Upright or inverted image • Real or virtual image • Use the thin lens equation to solve problems • Analyze simple situations in which the image formed by one lens is the object for another lens

  24. Thin Lens Shapes • These are examples of converging lenses • They have positive focal lengths • They are thickest in the middle

  25. More Thin Lens Shapes • These are examples of diverging lenses • They have negative focal lengths • They are thickest at the edges

  26. Thin Lenses • Converging Lenses • biconvex • convex-concave • plano-convex

  27. Thin Lenses

  28. Thin Lenses • Diverging Lenses • biconcave • convex-concave • plano-convex

  29. Thin Lenses

  30. Front side p positive q negative -------------- incident light Back side p negative q positive ------------- refracted light Ray Diagrams (Lenses)

  31. Sign Convention for Lenses • f is (+) for a converging lens • f is (-) for a diverging lens • R1 & R2 are (+) if the center of curvature is in back of the lens (converging) • R1 & R2 are (-) if the center of curvature is in front of the lens (diverging)

  32. Ray Diagrams (Lenses) • Steps for Drawing ray diagrams • Ray 1 is parallel to the principal axis & is refracted through one of the focal points • Ray 2 is drawn through the center of the lens and continues straight through. • Ray 3 is drawn through the other focal point, & emerges from the lens parallel to the principal axis

  33. Thin Lenses • Thin Lens Equation 1 + 1 = 2 pq R • Thin Lens Equation in terms of focal length 1 + 1 = 1 pqf

  34. Thin Lenses • Magnification Equation M = image height = h’ = - q object height h p

  35. Ray Diagrams for Lenses • Converging Lenses • Object behind the focal point • Object in front of the focal point • Diverging Lenses • Object behind the focal point • Object in front of focal point

  36. Combination of Thin Lenses • The image formed by the first lens is treated as the object for the second lens

  37. Chapter 23 Resources • http://www.physicsclassroom.com/Class/refrn/U14L5eb.html

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