1. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science The Geometric Optics of Image Formation

2. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science (I) Clear Materials Bend Rays Light bending is called "refraction". Water ray where a straight ray would come from. where the ray really comes from. Air

3. Imaging Science FundamentalsChester F. Carlson Center for Imaging ScienceRefraction Water n is low The amount of bending depends on a property of the material called "index of refraction", n. Glass n is high

4. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s VacuumRefraction

5. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s “wavefronts”Refraction

6. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s “wavefronts” separated by one wavelengthRefraction

7. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

8. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

9. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

10. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

11. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

12. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

13. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

14. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/sRefraction

15. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Velocity in other media is less than c: Mediumvelocity vacuum 3 x 10 8 m/s air 2.999 x 10 8 m/s water 2.26 x 10 8 m/s glass 2 x 10 8 m/s diamond 1.25 x 10 8 m/s Index of refraction

16. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science The index of refraction, n, of a medium is defined as the ratio of the speed of light in a vacuum to the speed in that medium: n = c/v Mediumvelocityn vacuum 3 x 10 8 m/s1 air 2.999 x 10 8 m/s1.0003 water 2.26 x 10 8 m/s1.33 glass 2 x 10 8 m/s1.5 diamond 1.25 x 10 8 m/s2.4 Index of refraction

17. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

18. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

19. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

20. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

21. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

22. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

23. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

24. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s The velocity of light in a vacuum is a fundamental constant: c = 3 x 10 8 m/s Glass: V = 200,000,000 m/sRefraction

25. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s Glass: V = 200,000,000 m/s

26. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Refraction for Different Materials  AIR WATER GLASS DIAMOND    light

27. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science MaterialIndex of Refraction, n Vacuum 1 (exactly) Air 1.0003 (approximately 1.000) Water 1.33 Glass 1.5 Diamond 2.4 11 22 n1n1 n2n2 Material #2 Material #1 Snell’s Law: n 1 sin  1 = n 2 sin  2 Examples

28. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Snell’s Law: The equations Snell’s Law: n 1 sin  1 = n 2 sin  2 Define n = 1 for a vacuum All other values of n are >1. 11 22 n1n1 n2n2 Material #2 Material #1

29. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Snell’s Law: n 1 sin  1 = n 2 sin  2 It works exactly the same in reverse. MaterialIndex of Refraction, n Vacuum 1 (exactly) Air 1.0003 (approximately 1.000) Water 1.33 Glass 1.5 Diamond 2.4 11 22 n1n1 n2n2 Material #2 Material #1

30. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Into and out of a flat plate of glass. Air, n 1 = 1.00 Glass n 2 = 1.5 Air, n 3 = 1.00 11 22 33 44 n 1 sin  1 = n 2 sin  2 n 3 sin  3 = n 4 sin  4

31. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science It can be shown that Air, n 1 = 1.00 Glass n 2 = 1.5 Air, n 3 = 1.00 11 22 33 44  1 =  4  2 =  3 and the input and output rays are parallel.

32. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Using Refraction to Focus Light. Glass Lens in Air n 1 =1 n 2 =1.5 Parallel Rays Focal point of lens Focal length of lens, f Optical Axis

33. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Glass Lens in Air n 1 =1 n 2 =1.5 Parallel Rays different direction Image Plane Parallel rays come to focus at one point on the image plane. Focal length of lens, f Optical Axis

34. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science A Chief Ray is a ray heading toward or away from the center of the lens. Glass Lens in Air n 1 =1 n 2 =1.5 Focal length of lens, f Examples of Chief Rays Optical Axis

35. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Thin Lens Approximation: Chief Rays pass through the lens without deviation. Glass Lens in Air n 1 =1 n 2 =1.5 Focal length of lens, f Examples of Chief Rays Optical Axis