Refractions, Reflections and Caustics : Basic Concepts Lecture #15

1. Refractions, Reflections and Caustics : Basic Concepts Lecture #15 Thanks to Henrik Jensen, John Hart, Ron Fedkiw, Pat Hanrahan, Rahul Swaminathan, Ko Nishino

2. Reflection and Refraction Reflection Vertex Normal N α α Air Water β Refraction

3. Snell’s Law • α Incoming = α Reflected • sin(α)/sin(β) = Refractive Index (material dependent) • Refractive index inversely proportional to speed of light (Huygens Principle)

8. Reflection

13. Really starts to be noticeable at less than 10-15° from the surface.

15. Fresnel Term • Fresnel Term as found in text books is F = ½ (sin²(α-β)/sin²(α+β)) + tan²(α-β)*tan²(α+β) • Returns good results for strong reflecting water surfaces

16. Approximated Fresnel Term • F0 = (N-1)2/(N+1)2 is a minimum of incoming light parallel to the normal of the surface. • Fα= F0+(1- cos(α))5 * (1- F0) is a value between 0 and 1 depending on the angle between the incoming ray and the surface normal. • e.g. F90 = 1, if the incoming ray is parallel to the surface, all light is reflected.

17. Designed to reflect all light eventually to Observer.

18. Anti-reflective Coatings • Reduce unwanted, stray reflections • Use material coatings on glass to reduce • reflection and maximize transmission. • Take advantage of destructive light interference. “One of the most significant advances made in modern lens design, whether for microscopes, cameras, or other optical devices, is the improvement in antireflection coating technology.”

19. Anti-reflective Coatings Magnesium fluoride very commonly used on Lenses, Microscopes

20. Refractions or Reflections?

21. Refractions or Reflections Confusion Why do you see shiny roads when they are diffuse and are not wet? Why do you see apparent reflections in deserts? Where else do you see apparent reflections? Do you see reflections above objects???

25. Used in Endoscopy, Communications

26. Water Drops : Refractions + Reflections

27. World in a drop A Drop and its Environment.

28. Shapes of falling drop Shapes of falling drop

29. L L e e ^ n ^ Refraction and Reflection ^ n ^ ^ s (s) i Image i plane q B ^ i q v q q A n a ^ z ^ r r a Pin hole q (r) z ^ p i

30. Refraction

31. Geometric mapping fov=165 degrees

32. Experiments: Refraction Experimental setup Calculated corners are in green

33. Photometry of Refraction

34. Plot of Transmitted Radiance

35. Experimental Setup difference image Rendered actual image Experiment: Photometry of Refraction

36. Reflection

37. Photometry of Reflection

38. Reflection vs. Refraction refraction 1 0.8 reflection 0.6 0.4 radiance L internal reflection 0.2 0 0 0 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1 1 distance from the center

39. Rendering a Rain drop

40. World in a Rain Drop Pupin Hall LowLibrary

41. Tired of water drops? Wait, there’s more…

42. Rainbows : Refractions + Reflections + Wavelength of Light

44. Visible Light Wavelength Dispersion

45. Can you see rainbows during midday?

46. Why are there two rainbows? Are there only two rainbows?

47. Why the color pattern?

48. Bright Sky under and Dark above the Rainbow Photo by Ben Lanterman taken immediately after a heavy rainstorm when the air was quite saturated at 4PM.

50. Caustics: Bunching up Reflections or Refractions