Ray Tracing

Step by step procedure in doing Ray Tracing Diagram for Plane Mirrors, Curved Mirrors, and Lenses. Bonus: Corrective Lens and Optical Devices are included in the presentation as well. Enjoy!

1. Image Formation on a Concave Mirror

2. Ray Diagram a  diagram  that traces the path that light takes in order for a person to view a point on the image of an object a technique used to determine the characteristics of the image formed by light on or by different surfaces.

3. Tips on Ray Diagram: We assume light to travel along straight paths, like the path of a particle as it travels along a medium.

4. Tips on Ray Diagram: As soon as light hits the REFLECTING surface of the mirror, it will, obviously, start to BOUNCE BACK.

5. Tips on Ray Diagram: The names of the major rays used describe the orientation of the INCIDENT RAY.

6. Parts of the ray diagram Notice that the shape is a circle and the diameter is what is called the “ optical axis ” Ensure that your circle has a perfect shape r

7. Parts of the ray diagram We shall be using only this part of the circle ALWAYS C is called center of curvature F is called the focal point B is called vertex C F V r focal length

8. How does a spherical concave mirror look like? Reflecting part is the INNER layer.

9. A concave mirror’s reflecting surface is on the ‘caved’ or ‘shrunken’ part of the mirror.

10. C F V Object object is placed beyond C

11. PARALLEL RAY Draw an Incident Ray that is PARALLEL to the Principal axis From the tip of the object and straight to the reflective surface C F V Object

12. PARALLEL RAY The reflected ray will bounce back in front of the mirror, passing through the focal point, F You may extend the line a little bit C F V Object

13. VERTEX RAY Draw an Incident Ray that directly hits the vertex of the mirror From the tip of the object and straight to V C F V Object

14. VERTEX RAY The reflected ray bounces back in front of the mirror following the Law of Reflection θ i = θ r You may use a protractor for this C F V Object θ i θ r

15. FOCAL RAY Draw an Incident Ray that passes through the focal point (F) and straight to the reflective surface Originating from the tip of the object C F V Object

16. FOCAL RAY The reflected ray bounces back in front of the mirror The ray is now parallel to the optical axis C F V Object

17. STRAIGHT RAY Draw an Incident Ray that passes through the center of curvature (C) and straight to the reflective surface (sometimes located outside of the actual mirror) C F V Object

18. PUTTING ALL TOGETHER PARALLEL RAY C F V Object VERTEX RAY FOCAL RAY STRAIGHT RAY

19. PUTTING ALL TOGETHER C F V Object The intersection of the three rays is now the tip of the image formed Image How would you describe the characteristics of the image?

20. DESCRIBING THE IMAGE FORMED C F V Object The image is described in terms of the following: Location Orientation Size Type Image

21. Location (the location of the image relative to the mirror) Between F and V At F Between F and C At C Beyond C

22. Location (the location of the image relative to the mirror) Location is also accurately measured if the ray diagram used an appropriate scale Exact measurements using a ruler or a protractor was used and the diagram was done on a graphing paper

23. Orientation (position of the object) Upright – if the image is mounted just like the object (formed above the optical axis) Inverted – if the image is mounted in the opposite direction as the object (formed below the optical axis)

24. Size (relates the size of the image compared to the object) Reduced – if the image looks smaller than the object Enlarged/ Magnified – if the image is bigger than the object

25. Type (based on the kind of reflected rays from which the image was formed) Real – if the image is formed in front of the mirror (real rays or solid lines were used) Virtual– if the image is formed behind/inside the mirror (virtual rays or broken lines were used)

26. Therefore, when an object is placed beyond the center of curvature of a concave mirror… The image formed is: Between C & F; Inverted; Reduced; and Real C F V

27. For your outputs, we can skip tracing the focal and straight rays We can rely on parallel and vertex rays for accuracy and simplicity C F V

28. Take Note! We will ALL use a focal length that is around 2 to 4 cm f = r / 2 Focal length is half of a radius r

29. Take Note! Cut out a piece of cardboard into a circle using this length Poke a hole at the center to mark your center of curvature Use this as your tracer curved mirrors r f

30. Practice Exercises! #2

31. Image Formation on a CONVEX Mirror

32. How does a spherical CONVEX mirror look like? Reflecting part is the OUTER layer.

33. A convex mirror’s reflecting surface is on the “bulging” part of the mirror.

34. The parts on the optical axis is now on the other side of the mirror They are all considered virtual An apostrophe is added to the symbol (‘) C’ F’ V ! SHIFT YOUR PERSPECTIVE

35. C’ F’ V Object F C object is placed between C & F

36. C’ F’ V Object PARALLEL RAY Draw an Incident Ray that is PARALLEL to the Principal axis F

37. C’ F’ V Object PARALLEL RAY Align the reflected ray to the focal point inside the mirror F

38. F C’ F’ V Object FOCAL RAY Draw an Incident Ray that is pointed directed to the virtual focal point (F’)

39. C’ F’ V Object FOCAL RAY But you must break the solid lines as soon as the ray hits the surface of the mirror F

40. C’ F’ V Object FOCAL RAY The direction of the incident ray should follow this path F

41. C’ F’ V Object FOCAL RAY The reflected ray bounces back parallel to the optical axis F

42. C’ F’ V Object FOCAL RAY Extend the reflected ray towards the inside of the mirror Use a different broken line pattern F

43. F C’ F’ V Object STRAIGHT RAY Draw an Incident Ray that is pointed directly to the virtual center of curvature, (C’)

44. C’ F’ V Object STRAIGHT RAY The incident ray is also the reflected ray so the arrow has two (2) arrow heads F

45. PUTTING ALL TOGETHER PARALLEL RAY FOCAL RAY STRAIGHT RAY C’ F’ V Object F

46. PUTTING ALL TOGETHER C’ F’ V Object How would you describe the characteristics of the image? Identifying where the intersection of the line is… F

47. C’ F’ V Object DESCRIBING THE IMAGE The image formed is: Between F’ & V; Upright; Reduced; and Virtual F

48. DESCRIBING THE IMAGE C’ F’ V F We can skip tracing the focal ray To keep it simple, we’ll work with parallel and straight rays

49. Practice Exercises! #3

50. Lesson Review! Answer on your notebook the questions on Page 105

51. FOLDABLES! Prepare a paper half the size of short bond paper. Please refer to the instructions on Page 102.

52. How can you demonstrate the law of reflection? When light strikes a mirror, the angle of reflection equals the angle of incidence. You can demonstrate the law of reflection by measuring the angles of incident and reflected light rays between an object and a mirror Go to page 106 and find a partner Reserve/prepare ALL the materials Follow the steps in the procedure Write your outputs on a short bond paper 30 minutes only!

53. REFRACTION AND LENSES LESSON 2

54. ESSENTIAL QUESTION What happens to light as it moves from one transparent substance to another?

55. ESSENTIAL QUESTION How do convex lenses and concave lenses affect light?

56. ESSENTIAL QUESTION How doe eyes detect light and color?

57. INQUIRY Name some objects that enable you to see small things. (See page 107)

58. WHAT HAPPENS TO LIGHT THAT PASES FROM ONE TRANSPARENT SUBSTANCE TO ANOTHER? Tasks: (Go to page 108) Prepare the materials Follow the steps in the procedure Answer the “Think About This” in a Size 2 CW paper (per lab group) 15 minutes only! Launch Lab

59. (1) The diagram for the first setup should show light traveling from the air/water/oil to glass (test tube) to water/oil to glass/beaker to air. POST-LAB DISCUSSION

60. light air glass water glass oil The light seemed to be bent

61. (2) The test tube with oil was not visible when it was immersed in oil, but it was visible when it was immersed in water. The test tubes with air and water were always visible. POST-LAB DISCUSSION

62. (2) The test tube with oil was not visible when it was immersed in oil, but it was visible when it was immersed in water. The test tubes with air and water were always visible. POST-LAB DISCUSSION

63. (2) The test tube with oil was not visible when it was immersed in oil, but it was visible when it was immersed in water. The test tubes with air and water were always visible. POST-LAB DISCUSSION

64. What DOES REFRACTION REFER TO? Bending of light as it passes from one medium to another

65. If the light moves into a transparent substance with a different index of refraction at 90° to the surface, it changes speed, but it does not change direction

66. If it enters at an angle other than 90°, it changes speed and changes direction. This is also known as refraction.

67. Index of refraction The index of refraction for a material is the ratio of the velocity of light, c, in a vacuum (3 x 108 m/s) to the velocity, v, through the material.  

68. Based on Table 1, which of the following media will make the light wave bend the most? Ice Water Glass Diamond

69. Which way will light move as it enters a medium that causes it to move more slowly? Towards the Normal line

70. Describe a situation in which a light ray would move away from the normal line while passing from one medium to another.

71. Image Formation THROUGH LENSES

72. Biconvex Lens (Converging Lens)

73. Convex Glass Surface C axis     A convex surface is called “converging” because parallel rays converge towards one another AIR (fast) GLASS (slow) normal line fast to slow bends towards the normal  

74. Convex Glass Surface C axis     The surface is converging for both air to glass rays and glass to air rays AIR GLASS normal line slow to fast bends away from the normal  

75. C axis     A concave surface is called “diverging” because parallel rays diverge away from one another Concave Glass Surface AIR GLASS

76. C axis     Again, the surface is diverging for both air to glass rays and glass to air rays Concave Glass Surface AIR GLASS

77. Converging Lens The focal point of a curved mirror was the image point of a distant star It is the same for a lens. The focal point of a converging lens is where the incoming rays from a distant star all intersect. A distant star is used to guarantee that the incoming rays are parallel Focal point Focal distance

78. F’ F Lenses optic axis 2F 2F principal axis secondary focal point primary focal point

79. F Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point

80. Thin Lenses Just as the ray tracing for mirrors is approximate and only accurate for certain situations, the ray tracing for lenses is accurate only for what are called “ thin lenses ” F’ F thickness of lens distance to focal point

81. How is the image formed by a converging lens?

82. Converging Lens: Ray Tracing Rules Rule 1: Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point. F F

83. Converging Lens: Ray Tracing Rules Rule 2: Rays passing through the center of the lens are undeflected , they continue straight through without being bent. Several rays are shown here as examples. F F

84. Converging Lens: Ray Tracing Rules Rule 3: The reverse of Rule 1, rays passing through the focal point are deflected to exit parallel to the axis F F

85. Major Rays used in Ray Tracing

86. The incident light ray from the object that is parallel to the principal axis will be refracted passing through the principal focal point after passing through the optic axis . Parallel Ray

87. F F’ 2F 2F’ Parallel Ray

88. The incident light ray that passes through the secondary focal point will be refracted parallel to the principal axis. Focal Ray

89. F F’ 2F 2F’ Focal Ray

90. The incident light ray that seems to pass through the optical center will not be refracted. Optic Ray

91. F F’ 2F 2F’ Optic Ray

92. F F’ 2F 2F’ Image

93. Practice Exercises! #4

94. Biconcave Lens (Diverging Lens)

95. F’ F In diverging lens, parallel rays are deflected such that when extended backwards, they appear to be coming from the focal point on the other side. Diverging Lens

96. Diverging Lens: Ray Tracing F’ F Parallel rays are deflected so they appear to be coming from the focal point in front of the lens.

97. Diverging Lens: Ray Tracing F’ F Just like for converging lenses, rays that pass through the center of the lens continue undeflected (straight) through the lens.

98. Diverging Lens: Ray Tracing F’ F Rays that, if extended, would pass through the focal point on the other side of the lens, are deflected to be parallel to the axis.

99. Major Rays used in Ray Tracing

100. The incident light ray from the object that is parallel to the principal axis will be refracted as if it came from the secondary focal point . Parallel Ray

101. F F’ 2F 2F’ Parallel Ray

102. The incident light ray that seems to pass through the principal focal point will be refracted parallel to the principal axis . Focal Ray

103. F F’ 2F 2F’ Focal Ray

104. The incident light ray that seems to pass through the optical center will not be refracted. Optic Ray

105. F F’ 2F 2F’ Optic Ray

106. F F’ 2F 2F’ Image

107. Practice Exercises! #5

108. OPTICAL DEVICES

109. wikipedia.org Microscope

110. etsy.com Spyglass

111. bebusinessed.com Telescope

112. wikipedia.org Camera

113. bhphotovideo.com Camera

114. evolutionnews.com Human eye

115. Seatwork! Draw a ray diagram on the ff. optical devices: Camera Human eye Spyglass Microscope Telescope Periscope

116. Corrective lenses

117. Corrective Lenses: Myopia To correct myopia ( nearsightedness ), a diverging lens creates an intermediate image of a distant star at your far point so that your eye can see it even though the star is beyond your far point.

118. Corrective Lenses: Myopia To correct myopia ( nearsightednes s), a diverging lens creates an intermediate image of a distant star at your far point so that your eye can see it even though the star is beyond your far point. far point image of distant object

119. Corrective Lenses: Hyperopia To correct farsightedness your contact lens creates an (intermediate) image of a book 25 cm away at your near point so that your farsighted eye can see it even though the book is closer than your near point 25 cm near point

120. Corrective Lenses: Hyperopia To correct farsightedness your contact lens creates an (intermediate) image of a book 25 cm away at your near point so that your farsighted eye can see it even though the book is closer than your near point near point 25 cm focal point of corrective lens