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Reflections in Curved Mirrors (old version)

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Reflections in Curved Mirrors (old version)

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 <ul><li>Concave </li></ul>Convex “converging” mirror “diverging” mirror
3. 3. Convex & Concave Mirrors <ul><li>Which part of this circle is showing a convex mirror? </li></ul><ul><li>Which part is a concave mirror? </li></ul><ul><li>How did you know? </li></ul>Hint: You must first identify where the light rays are coming from and thus locating the reflective surface.
4. 4. Convex & Concave Mirrors Concave mirror Convex mirror <ul><li>Concave mirrors are shaped like part of the inside of a sphere </li></ul><ul><li>Convex mirrors are shaped like part of the outside of a sphere </li></ul>Centre of sphere
5. 5. Terminology <ul><li>Center of Curvature (C) </li></ul><ul><li>the centre of the sphere whose surface forms the curved mirror </li></ul><ul><li>Principal Axis </li></ul><ul><li>the straight line passing through the centre of curvature to the mirror (radius of sphere) </li></ul><ul><li>Vertex (V) or Pole (P) </li></ul><ul><li>the point where the principal axis meets the mirror </li></ul>
6. 6. Terminology <ul><li>Normal </li></ul><ul><li>the straight line joining any point on a curved mirror with the centre of curvature </li></ul><ul><li>Notice it is the same as the radius and principle axis </li></ul>
7. 7. <ul><li>Focal Point or Focus (F) - where the light rays meet, located at half the distance between centre of curvature and mirror (1/2 radius) </li></ul><ul><li>Focal Length ( f ) - the distance from the focal point to the vertex </li></ul><ul><li>Note: the distance from C to the vertex is 2f </li></ul>Terminology principal axis vertex f C
8. 8. Concave Mirrors
9. 9. Concave Mirrors <ul><li>Surface of mirror is curved inwards forming a ‘cave’ </li></ul><ul><li>Concentrates light rays </li></ul><ul><li>Also known as converging mirror </li></ul><ul><li>Produces a 3 different types of images </li></ul>
10. 10. Applications of Concave Mirrors
11. 11. Applications of Concave Mirrors
12. 12. Light Rays with Concave Mirrors <ul><li>A light ray parallel to the principal axis is reflected through F </li></ul><ul><li>Notice how all the rays converge at F </li></ul><ul><li>That’s why concave mirrors are also known as converging mirrors </li></ul>
13. 13. <ul><li>A light ray parallel to the principal axis is reflected through F </li></ul>C F h C F h C F h C F h
14. 14. Light Rays with Concave Mirrors <ul><li>A light ray parallel to the principal axis is reflected through F </li></ul><ul><li>A light ray through F will reflect parallel to the principle axis </li></ul>
15. 15. 2) A light ray through F will reflect parallel to the principle axis C F h C F h C F h C F h
16. 16. Light Rays with Concave Mirrors <ul><li>A light ray parallel to the principal axis is reflected through F </li></ul><ul><li>A light ray through F will reflect parallel to the principle axis </li></ul><ul><li>A light ray through C is reflected back onto itself </li></ul>
17. 17. 3) A light ray through C is reflected back onto itself C F h C F h C F h C F h
18. 18. Why do rays that go through the centre of curvature reflect back on itself? <ul><li>Any line through C is the same as the …. of a circle </li></ul><ul><li>The line through C has an angle of …. relative to the mirror </li></ul><ul><li>This line is also known as …. </li></ul><ul><li>The angle of …. equals the angle of incidence which explains why this line reflects back on itself </li></ul>
19. 19. Light Rays with Concave Mirrors <ul><li>A light ray parallel to the principal axis is reflected through F </li></ul><ul><li>A light ray through F will reflect parallel to the principle axis </li></ul><ul><li>A light ray through C is reflected back onto itself </li></ul><ul><li>A light ray aimed at the vertex will follow the Law of Reflection </li></ul>
20. 20. 4) A light ray aimed at the vertex will follow the Law of Reflection (angle of incidence = angle of reflection) C F h C F h C F h C F h
21. 21. LOCATING AN IMAGE ON A CONCAVE MIRROR <ul><li>Any two light rays from the same location off an object is needed to locate its image </li></ul><ul><li>A light ray parallel to the principal axis is reflected through F </li></ul><ul><li>A light ray through F will reflect parallel to the principle axis </li></ul><ul><li>A light ray through C is reflected back onto itself </li></ul><ul><li>A light ray aimed at the vertex will follow the Law of Reflection </li></ul>
22. 22. LOCATING AN IMAGE ON A CONCAVE MIRROR <ul><li>Ray 1 - travels parallel to the principal axis and reflects through the focal point (F) </li></ul>
23. 23. LOCATING AN IMAGE ON A CONCAVE MIRROR <ul><li>Ray 2 - travels through the focal point and reflects parallel to the principal axis </li></ul>
24. 24. LOCATING AN IMAGE ON A CONCAVE MIRROR <ul><li>The point where the two reflected rays converge will be the location of the image </li></ul>
25. 25. LOCATING AN IMAGE ON A CONCAVE MIRROR <ul><li>5 Scenarios for the Object </li></ul><ul><li>Beyond C: Object is greater than 2 focal lengths from the mirror (d o >2 f ) </li></ul><ul><li>At C: Object is at the centre of curvature (d o =2 f ) </li></ul><ul><li>Between C and F: Object is between 1 and 2 focal lengths from the mirror (f< d o <2 f ) </li></ul><ul><li>At F: Object is at the focal point (d o = f ) </li></ul><ul><li>Between F and mirror: Object is between the mirror and the focal point (0<d o < f ) </li></ul>
26. 26. Case 1 – Object Beyond C Reduced Inverted Between C & F Real Location Size Attitude Type
27. 27. Case 2 – Object at C Same Inverted At C Real Location Size Attitude Type
28. 28. Case 3 – Object between C & F Enlarged Inverted Beyond C Real Location Size Attitude Type
29. 29. Case 4 – Object at F No Image Formed! Location Size Attitude Type
30. 30. Case 5 Object between F & mirror Enlarged Upright Behind mirror Virtual Location Size Attitude Type
31. 31. Convex Mirrors
32. 32. Curved Mirrors <ul><li>Concave </li></ul>Convex “converging” mirror “diverging” mirror
33. 34. Convex Mirrors <ul><li>Surface of mirror is curved outward </li></ul><ul><li>Spreads out light rays </li></ul><ul><li>Also known as diverging mirror </li></ul><ul><li>Produces a virtual image that is upright and smaller than the object </li></ul>
34. 35. Applications of Convex Mirrors
35. 36. Light Rays with Convex Mirrors <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul>
36. 37. Light Rays with Convex Mirrors <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul>
37. 38. <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul>F C h
38. 39. Light Rays with Convex Mirrors <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul><ul><li>A ray aimed at F is reflected parallel to the principal axis </li></ul>
39. 40. 2) A ray aimed at F is reflected parallel to the principal axis F C h
40. 41. Light Rays with Convex Mirrors <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul><ul><li>A ray aimed at F is reflected parallel to the principal axis </li></ul><ul><li>A ray aimed at C is reflected back upon itself </li></ul>
41. 42. 3) A ray aimed at C is reflected back upon itself F C h
42. 43. Light Rays with Convex Mirrors <ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul><ul><li>A ray aimed at F is reflected parallel to the principal axis </li></ul><ul><li>A ray aimed at C is reflected back upon itself </li></ul><ul><li>A light ray aimed at the vertex will follow the Law of Reflection </li></ul>
43. 44. 4) A light ray aimed at the vertex will follow the Law of Reflection F C h
44. 45. LOCATING AN IMAGE ON A CONVEX MIRROR <ul><li>Any two light rays off the same location on the object are needed to locate an image </li></ul><ul><li>A ray parallel to the principal axis is reflected as if it had come through F </li></ul><ul><li>A ray aimed at F is reflected parallel to the principal axis </li></ul><ul><li>A ray aimed at C is reflected back upon itself </li></ul><ul><li>A light ray aimed at the vertex will follow the Law of Reflection </li></ul>
45. 46. LOCATING AN IMAGE ON A CONVEX MIRROR <ul><li>Ray 1: travels parallel to the principal axis and reflects through the focal point </li></ul>BEFORE AFTER
46. 47. LOCATING AN IMAGE ON A CONVEX MIRROR <ul><li>Ray 2: travels towards the focal point and reflects parallel to the principal axis </li></ul>BEFORE AFTER
47. 48. LOCATING AN IMAGE ON A CONVEX MIRROR <ul><li>The image appears where the (virtual) reflected rays appear to intersect </li></ul>
48. 49. Remember : The image for a convex mirror is always virtual, upright and smaller!
49. 50. Try it! <ul><li>Draw the light rays. </li></ul><ul><li>Draw the image. </li></ul>
50. 52. Locating an Image in a Curved Mirror <ul><li>Pick a point on the object (usually the top of the object). </li></ul><ul><li>Send any two incident rays off the point on the object (follow the light ray rules for curved mirrors choosing 2 of 4 possibilities). </li></ul><ul><li>Draw the reflected ray as a solid line (on the same side of the mirror as the object). </li></ul><ul><li>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. </li></ul><ul><li>Use the point of intersection to locate the image. Draw the image. </li></ul>