1. Corner Cube or Retro Reflectors These Corner Cube or Retro Reflectors are resource material to support parts of STAO’s ScienceWorks Grade 10 Optics The following are excerpts from L4 The Laws of Reflection (Slides 34 to 57 of 74)

2. Corner Cube or Retro Reflectors When light is shone on them from something like a car (Incident rays) it is reflected straight back toward the car. The Reflected rays are parallel and in the opposite direction of Incident rays. Corner Cube Reflectors,are used in Bicycle Reflectors Bicycle Reflectors

3. Why not just use a mirror to reflect light back into the Eye/Brain? Bicycle Reflectors

4. Slight changes in the mirrors orientation would cause the reflected light to miss the Eye/Brain?

5. Bicycle Reflectors Slight changes in the mirrors orientation would cause the reflected light to miss the Eye/Brain?

6. Bicycle Reflectors If two mirrors are arranged at 90 º, slight changes in the mirrors orientation do not affect the direction of the reflected light.

7. Bicycle Reflectors If two mirrors are arranged at 90 º, slight changes in the mirrors orientation do not affect the direction of the reflected light.

8. Bicycle Reflectors - Mathematical Proof 1)Use the laws of reflection and geometry to prove light is reflected back, parallel to the incident ray from two mirrors at right angles?

9. At B, let the first Angle of Incidence = Angle of Reflection = x or (  i =  r = x) Bicycle Reflectors - Mathematical Proof

10. At C, let the second Angle of Incidence = Angle of Reflection = y or (  i =  r = y) Bicycle Reflectors - Mathematical Proof

11. Note  A= 90 º In ∆ABC,  A+x+y = 180 º 90 º +x+y = 180 º  x+y = 90 º The Transversal line BC 2x+2y = 2(x+y) = 2(90 º ) = 180 º  Lines IB and CR are parallel because the interior angles on the same side of the transversal are supplementary Bicycle Reflectors - Mathematical Proof

12. This proof is only in two dimensions. Bicycle Reflectors - Mathematical Proof In two dimensions, this only proves that the Incident and Reflected rays are on parallel planes (yellow). The rays could be drawn on planes (yellow) perpendicular to (in & out of) the page.

13. All light is reflected in horizontal planes. No light is lost to up and down reflections Looking from above, the two mirrors act like a single mirror as far as the horizontal direction of the reflected ray is concerned. Bicycle Reflectors - Mathematical Proof

14. Slight changes in the two mirrors horizontal orientation would cause the reflected light to miss the Eye/Brain? Bicycle Reflectors - Mathematical Proof

15. Bicycle Reflectors - Mathematical Proof Slight changes in the two mirrors horizontal orientation would cause the reflected light to miss the Eye/Brain?

16. Bicycle Reflectors - Mathematical Proof Slight changes in the two mirrors horizontal orientation would cause the reflected light to miss the Eye/Brain?

17. But All light is reflected in a horizontal plane. No light is lost to vertical reflections so all Eye/Brains see bright reflected light. Bicycle Reflectors - Mathematical Proof

18. If three mirrors are arranged like the corner of a cube,they are called “ corner cube reflector ” or a “ retro reflector ”. They are all at right angles to each other,

19. In corner cube reflectors,the Incident ray and final Reflected ray are parallel lines. They are in exactly opposite directions. But the light must reflect form each of the three mirrors

20. Measuring the Distance to the Moon Laser ranging Corner Cube Reflectors were positioned on the Moon in 1969 by the Apollo 11 astronauts. Laser pulses beamed at the reflectors from Earth, help scientists determine the distance between the earth and Moon to an accuracy of about 3 centimeters.

21. Precut Corner Cube Reflector mirrors are available at STAO Store. The following shows how to finish assembling them. All mirrors will last a very long time if the back is covered with duct tape. BUT Be careful you do not damage the coating on the back by trying to remove or adjust duct tape. You can often obtain scrap glass mirrors from Window & Mirror companies at reasonable prices. Seeing Things Making Corner Cube or Retro Reflectors

22. The Precut Corner Cube Reflector mirrors are shipped flat in order to reduce shipping costs. They look like the above picture

23. Seeing Things Making Corner Cube or Retro Reflectors Fold the top two corners together as shown in the next series of slides

24. Seeing Things Making Corner Cube or Retro Reflectors Fold the top two corners together as shown in the next series of slides

25. Seeing Things Making Corner Cube or Retro Reflectors Fold the top two corners together as shown in the next series of slides

26. Seeing Things Making Corner Cube or Retro Reflectors Fold the top two corners together as shown in the next series of slides

27. Seeing Things Making Corner Cube or Retro Reflectors Flip over and

28. Seeing Things Making Corner Cube or Retro Reflectors Flip over and duct tape the back

29. Seeing Things Making Corner Cube or Retro Reflectors Flip over and duct tape the back

30. Seeing Things Making Corner Cube or Retro Reflectors Flip over and duct tape the back

31. Seeing Things Making Corner Cube or Retro Reflectors Trim the access duct tape from the back

32. Seeing Things Making Corner Cube or Retro Reflectors If you have extra small square mirrors you can also make your own corner cube reflector. If possible use triangular mirrors.

33. Seeing Things Making Corner Cube or Retro Reflectors Dust tape the first two mirrors at 90°.

34. Seeing Things Making Corner Cube or Retro Reflectors Dust tape the first two mirrors at 90°.

35. Seeing Things Making Corner Cube or Retro Reflectors Dust tape the first two mirrors at 90°.

36. Seeing Things Making Corner Cube or Retro Reflectors Dust tape the first two mirrors at 90°.

37. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirror on top

38. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

39. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

40. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

41. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

42. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

43. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

44. Seeing Things Making Corner Cube or Retro Reflectors Place the next mirrors on top and duct tape

45. Seeing Things Making Corner Cube or Retro Reflectors Flip over

46. Seeing Things Making Corner Cube or Retro Reflectors This is the corner cube reflector

47. Seeing Things Making Corner Cube or Retro Reflectors This is the corner cube reflector that is nearly identical to purchased ones

48. The area outside the dotted lines can cause confusion as the light ray must reflect from all mirrors if it is to reflect directly back at the origin of the incident ray.

49. Bicycle reflectors use this shape to reflect light back light ray must reflect from all mirrors if it is to reflect directly back at the incident ray

51. Bicycle Reflectors and the Distance to the Moon In other words, Check it out! Does the theory work? Arrange three mirrors so they form the corner of a cube. Then shine a laser pointer at them and see if it’s reflected back regardless of the direction you shine the laser. Misting with a spray bottle will make the laser beam visible. Try a Bicycle Reflector It is certainly true that principles cannot be more securely founded than on experience and consciously clear thinking. — Albert Einstein