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# 14 ray diagrams

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• When doing geometric optics problems it is much simpler to draw the lens/mirror as a line so that the light relects/refracts at the line. This saves us from having to show the lights behavior inside the lens.
• ### 14 ray diagrams

1. 1. Ray Diagrams J.M. Gabrielse
2. 2. Outline • Reflection • Mirrors • Plane mirrors • Spherical mirrors • Concave mirrors • Convex mirrors • Refraction • Lenses • Concave lenses • Convex lenses J.M. Gabrielse
3. 3. A ray of light is an extremely narrow beam of light. J.M. Gabrielse
4. 4. All visible objects emit or reflect light rays in all directions. J.M. Gabrielse
5. 5. Our eyes detect light rays. J.M. Gabrielse
6. 6. We see images when light rays converge in our eyes. converge: come together J.M. Gabrielse
7. 7. Mirrors It is possible to see images in mirrors. image object J.M. Gabrielse
8. 8. Reflection (bouncing light) normal Reflection is when light changes direction by bouncing off a surface. When light is reflected off a mirror, it hits the mirror at the same angle (the incidence angle, θi) as it reflects off the mirror (the reflection angle, θr). The normal is an imaginary line which lies at right angles to the mirror where the ray hits it. reflected ray incident ray θr θi Mirror J.M. Gabrielse
9. 9. Mirrors reflect light rays. J.M. Gabrielse
10. 10. Plane Mirrors (flat mirrors) How do we see images in mirrors? J.M. Gabrielse
11. 11. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. J.M. Gabrielse
12. 12. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. The eye perceives light rays as if they came through the mirror. Imaginary light rays extended behind mirrors are called sight lines. J.M. Gabrielse
13. 13. Plane Mirrors (flat mirrors) object image How do we see images in mirrors? Light reflected off the mirror converges to form an image in the eye. The eye perceives light rays as if they came through the mirror. Imaginary light rays extended behind mirrors are called sight lines. The image is virtual since it is formed by imaginary sight lines, not real light rays. J.M. Gabrielse
14. 14. Spherical Mirrors (concave & convex) J.M. Gabrielse
15. 15. Concave & Convex (just a part of a sphere) • C r • F f C: the center point of the sphere r: radius of curvature (just the radius of the sphere) F: the focal point of the mirror (halfway between C and the mirror) f: the focal distance, f = r/2 J.M. Gabrielse
16. 16. Concave Mirrors (caved in) • F optical axis Light rays that come in parallel to the optical axis reflect through the focal point. J.M. Gabrielse
17. 17. Concave Mirror (example) • F optical axis J.M. Gabrielse
18. 18. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
19. 19. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
20. 20. Concave Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. A real image forms where the light rays converge. J.M. Gabrielse
21. 21. Concave Mirror (example 2) • F optical axis J.M. Gabrielse
22. 22. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
23. 23. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
24. 24. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The image forms where the rays converge. But they don’t seem to converge. J.M. Gabrielse
25. 25. Concave Mirror (example 2) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. A virtual image forms where the sight rays converge. J.M. Gabrielse
26. 26. Your Turn (Concave Mirror) object • F optical axis concave mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
27. 27. Your Turn (Concave Mirror) object • F optical axis concave mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
28. 28. Convex Mirrors (curved out) • F optical axis Light rays that come in parallel to the optical axis reflect from the focal point. The focal point is considered virtual since sight lines, not light rays, go through it. J.M. Gabrielse
29. 29. Convex Mirror (example) • F optical axis J.M. Gabrielse
30. 30. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. J.M. Gabrielse
31. 31. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. J.M. Gabrielse
32. 32. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
33. 33. Convex Mirror (example) • F optical axis The first ray comes in parallel to the optical axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the optical axis. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
34. 34. Your Turn (Convex Mirror) • F object optical axis convex mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
35. 35. Your Turn (Convex Mirror) object image • F optical axis convex mirror • Note: mirrors are thin enough that you just draw a line to represent the mirror • Locate the image of the arrow J.M. Gabrielse
36. 36. Lensmaker’s Equation 1 1 1 = + f di do ƒ = focal length do = object distance di = image distance if distance is negative the image is behind the mirror J.M. Gabrielse
37. 37. Magnification Equation hi − di m= = ho do m = magnification hi = image height ho = object height If height is negative the image is upside down if the magnification is negative the image is inverted (upside down) J.M. Gabrielse
38. 38. Refraction (bending light) Refraction is when light bends as it passes from one medium into another. normal air θi When light traveling through air passes into the glass block it is refracted towards the normal. glass block θr When light passes back out of the glass into the air, it is refracted away from the normal. Since light refracts when it changes mediums it can be aimed. Lenses are shaped so light is aimed at a focal point. θi θr normal air J.M. Gabrielse
39. 39. Lenses The first telescope, designed and built by Galileo, used lenses to focus light from faraway objects, into Galileo’s eye. His telescope consisted of a concave lens and a convex lens. light from object convex lens concave lens Light rays are always refracted (bent) towards the thickest part of the lens. J.M. Gabrielse
40. 40. Concave Lenses Concave lenses are thin in the middle and make light rays diverge (spread out). • F optical axis If the rays of light are traced back (dotted sight lines), they all intersect at the focal point (F) behind the lens. J.M. Gabrielse
41. 41. Concave Lenses • F optical axis Light rays that come in parallel to the opticalignore the thickness offocallens. The light rays behave the same way if we axis diverge from the the point. J.M. Gabrielse
42. 42. Concave Lenses • F optical axis Light rays that come in parallel to the optical axis still diverge from the focal point. J.M. Gabrielse
43. 43. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. J.M. Gabrielse
44. 44. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. J.M. Gabrielse
45. 45. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
46. 46. Concave Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts from the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
47. 47. Your Turn (Concave Lens) object • F optical axis concave lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
48. 48. Your Turn (Concave Lens) object • Fimage optical axis concave lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
49. 49. Convex Lenses Convex lenses are thicker in the middle and focus light rays to a focal point in front of the lens. The focal length of the lens is the distance between the center of the lens and the point where the light rays are focused. J.M. Gabrielse
50. 50. Convex Lenses • F optical axis J.M. Gabrielse
51. 51. Convex Lenses • F optical axis Light rays that come in parallel to the optical axis converge at the focal point. J.M. Gabrielse
52. 52. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. J.M. Gabrielse
53. 53. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. J.M. Gabrielse
54. 54. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. J.M. Gabrielse
55. 55. Convex Lens (example) • F optical axis The first ray comes in parallel to the optical axis and refracts through the focal point. The second ray goes straight through the center of the lens. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge. J.M. Gabrielse
56. 56. Your Turn (Convex Lens) • F object optical axis image convex lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
57. 57. Your Turn (Convex Lens) • F object optical axis image convex lens • Note: lenses are thin enough that you just draw a line to represent the lens. • Locate the image of the arrow. J.M. Gabrielse
58. 58. Thanks/Further Info • Faulkes Telescope Project: Light & Optics by Sarah Roberts • Fundamentals of Optics: An Introduction for Beginners by Jenny Reinhard • PHET Geometric Optics (Flash Simulator) • Thin Lens & Mirror (Java Simulator) by Fu-Kwun Hwang J.M. Gabrielse