Reflections in curved mirrors

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Reflections in curved mirrors

  1. 1. Curved Mirrors Concave Convex http://cuttingedgeartist.files.wordpress.com/2010/11/cloud-gate.jpg http://www.sculpture-info.com/upload/1008/image/1(2).jpg
  2. 2. Curved Mirrors Concave “converging” mirror Convex “diverging” mirror
  3. 3. Convex & Concave Mirrors  Which part of this circle is showing a convex mirror?  Which part is a concave mirror?  How did you know? Hint: You must first identify where the light rays are coming from and thus locating the reflective surface.
  4. 4. Convex & Concave Mirrors  Convex mirrors are shaped like part of the outside of a sphere  Concave mirrors are shaped like part of the inside of a sphere Centre of sphere Concave mirror Convex mirror
  5. 5. Terminology Center of Curvature (C)  the centre of the sphere whose surface forms the curved mirror Principal Axis  the straight line passing through the centre of curvature to the mirror (radius of sphere) Vertex (V) or Pole (P)  the point where the principal axis meets the mirror
  6. 6. Terminology Normal  the straight line joining any point on a curved mirror with the centre of curvature  Notice it is the same as the radius and principle axis
  7. 7. Terminology  Focal Point or Focus (F) - where the light rays meet, located at half the distance between centre of curvature and mirror (1/2 radius)  Focal Length (f) - the distance from the focal point to the vertex  Note: the distance from C to the vertex is 2f vertex principal axis C f
  8. 8. Concave Mirrors
  9. 9. Concave Mirrors  Surface of mirror is curved inwards forming a ‘cave’  Concentrates light rays  Also known as converging mirror  Produces a 3 different types of images
  10. 10. Applications of Concave Mirrors
  11. 11. Applications of Concave Mirrors
  12. 12. Light Rays with Concave Mirrors 1. A light ray parallel to the principal axis is reflected through F   Notice how all the rays converge at F That’s why concave mirrors are also known as converging mirrors
  13. 13. 1. A light ray parallel to the principal axis is reflected through F h C C F h F h C C F F h
  14. 14. Light Rays with Concave Mirrors 1. A light ray parallel to the principal axis is reflected through F 2. A light ray through F will reflect parallel to the principle axis
  15. 15. Light Rays with Concave Mirrors 2. A light ray through F will reflect parallel to the principle axis  Notice how all the rays reflect parallel
  16. 16. 2. A light ray through F will reflect parallel to the principle axis h C C F h F h C C F F h
  17. 17. Light Rays with Concave Mirrors 1. A light ray parallel to the principal axis is reflected through F 2. A light ray through F will reflect parallel to the principle axis 3. A light ray through C is reflected back onto itself
  18. 18. Light Rays with Concave Mirrors 3. A light ray through C is reflected back onto itself  Why do rays that go through the centre of curvature reflect back on itself? Centre of curvature = centre of sphere
  19. 19. Why do rays that go through the centre of curvature reflect back on itself?  Any line through C is the same as the …. of a circle  The line through C has an angle of …. relative to the mirror  This line is also known as ….  The angle of …. equals the angle of incidence which explains why this line reflects back on itself
  20. 20. 3. A light ray through C is reflected back onto itself h C C F h F h C C F F h
  21. 21. Light Rays with Concave Mirrors 1. A light ray parallel to the principal axis is reflected through F 2. A light ray through F will reflect parallel to the principle axis 3. A light ray through C is reflected back onto itself 4. A light ray aimed at the vertex will follow the Law of Reflection
  22. 22. 4. A light ray aimed at the vertex will follow the Law of Reflection (angle of incidence = angle of reflection) h C C F h F h C C F F h
  23. 23. Locating an Image in a Concave Mirror Any two light rays from the same location off an object is needed to locate its image 1. A light ray parallel to the principal axis is reflected through F 2. A light ray through F will reflect parallel to the principle axis 3. A light ray through C is reflected back onto itself 4. A light ray aimed at the vertex will follow the Law of Reflection
  24. 24. Locating an Image in a Concave Mirror  Ray 1 - travels parallel to the principal axis and reflects through the focal point (F)
  25. 25. Locating an Image in a Concave Mirror  Ray 2 - travels through the focal point and reflects parallel to the principal axis
  26. 26. Locating an Image in a Concave Mirror  The point where the two reflected rays converge will be the location of the image
  27. 27. Locating an Image in a Concave Mirror  5 regions where object could exist:
  28. 28. Locating an Image in a Concave Mirror 5 regions where object could exist: 1. Beyond C: Object is greater than 2 focal lengths from the mirror (do>2f) 2. At C: Object is at the centre of curvature (do=2f) 3. Between C and F: Object is between 1 and 2 focal lengths from the mirror (f<do<2f) 4. At F: Object is at the focal point (do=f) 5. Between F and mirror: Object is between the mirror and the focal point (0<do<f)
  29. 29. Case 1 – Object Beyond C Size Attitude Location Type Reduced Inverted Betwee nC&F Real
  30. 30. Case 2 – Object at C Size Attitude Location Type Same Inverted At C Real
  31. 31. Case 3 – Object between C & F Size Attitude Enlarge Inverted d Location Type Beyond C Real
  32. 32. Case 4 – Object at F Size Attitude Location No Image Formed! Type
  33. 33. Case 5 – Object between F & mirror Size Enlarge d Attitude Upright Location Behind mirror Type Virtu al
  34. 34. Convex Mirrors
  35. 35. Curved Mirrors Concave “converging” mirror Convex “diverging” mirror
  36. 36. Convex Mirrors     Surface of mirror is curved outward Spreads out light rays Also known as diverging mirror Produces a virtual image that is upright and smaller than the object
  37. 37. Applications of Convex Mirrors
  38. 38. Light Rays with Convex Mirrors 1. A ray parallel to the principal axis is reflected as if it had come through F
  39. 39. Light Rays with Convex Mirrors 1. A ray parallel to the principal axis is reflected as if it had come through F
  40. 40. 1. A ray parallel to the principal axis is reflected as if it had come through F h F C
  41. 41. Light Rays with Convex Mirrors 1. A ray parallel to the principal axis is reflected as if it had come through F 2. A ray aimed at F is reflected parallel to the principal axis
  42. 42. Light Rays with Convex Mirrors 2. A ray aimed at F is reflected parallel to the principal axis
  43. 43. 2. A ray aimed at F is reflected parallel to the principal axis h F C
  44. 44. Light Rays with Convex Mirrors 1. A ray parallel to the principal axis is reflected as if it had come through F 2. A ray aimed at F is reflected parallel to the principal axis 3. A ray aimed at C is reflected back upon itself
  45. 45. 3. A ray aimed at C is reflected back upon itself h F C
  46. 46. Light Rays with Convex Mirrors 1. A ray parallel to the principal axis is reflected as if it had come through F 2. A ray aimed at F is reflected parallel to the principal axis 3. A ray aimed at C is reflected back upon itself 4. A light ray aimed at the vertex will follow the Law of Reflection
  47. 47. 4. A light ray aimed at the vertex will follow the Law of Reflection h F C
  48. 48. Locating an Image in a Convex Mirror Any two light rays off the same location on the object are needed to locate an image 1. A ray parallel to the principal axis is reflected as if it had come through F 2. A ray aimed at F is reflected parallel to the principal axis 3. A ray aimed at C is reflected back upon itself 4. A light ray aimed at the vertex will follow the Law of Reflection
  49. 49. Locating an Image in a Convex Mirror BEFORE AFTER  Ray 1: travels parallel to the principal axis and reflects through the focal point
  50. 50. Locating an Image in a Convex Mirror BEFORE AFTER  Ray 2: travels towards the focal point and reflects parallel to the principal axis
  51. 51. Locating an Image in a Convex Mirror  The image appears where the (virtual) reflected rays appear to intersect
  52. 52. Locating an Image in a Convex Mirror Size Reduced Attitude Upright Location Behind mirror Type Virtual
  53. 53. Try it!  Draw the light rays.  Draw the image.
  54. 54. Locating an Image in a Curved Mirror 1. Pick a point on the object (usually the top of the object). 2. Send any two incident rays off the point on the object (follow the light ray rules for curved mirrors choosing 2 of 4 possibilities). 3. Draw the reflected ray as a solid line (on the same side of the mirror as the object). 4. Find the intersection of the reflected rays. If the rays do not intersect, extend the reflected rays into the virtual side of the mirror (use dotted line) until they do. 5. Use the point of intersection to locate the image. Draw the image.

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