1. S-95 Explain how a curved mirror, and a curved lens are different. Think in terms of image formation and in terms of what light photons do.

2. Geometric Optics AP Physics Chapter 23

3. Geometric Optics 23.1 The Ray Model of Light

4. Light travels in a straight line in most cases (away from very large gravitational fields) Ray Model – Light travels in straight line pathways called rays represents a narrow beam of light 23.1

5. 23.1 The Ray Model of Light We see an object when rays of light come from the object to our eyes 23.1

6. Geometric Optics 23.2 Reflection: Image Formation by a Plane Mirror

7. 23.2 Reflection When light strikes an object it is Reflected – bounces off Refracted – transmitted through Absorbed – converted to a different form of energy Law of Reflection 23.2

8. 23.2 Reflection Diffuse Reflection – on a rough surface Rays don’t form an pattern We see color Specular Reflection – smooth surface Patterns form images 23.2

9. S-101 Draw a ray diagram for a cat standing in front of a mirror. Use geometry to figure out the shortest possible mirror that will allow the cat to see his entire height.

10. 23.2 Reflection How are images formed Your eye sees the intersection of rays from an object 23.2 Applet

11. 23.2 Reflection Object Distance – from mirror to the object Image Distance – from mirror to the image Virtual Image – imaginary intersection of light rays Real Image – actual intersection of light 23.2

12. S-94 Two mirrors are placed facing each other. Use a point between the dots, and ray diagrams, determine the image distance in the second mirror. That is the image of the image in the first mirror.

13. Geometric Optics 23.3 Formation of Images by Spherical Mirrors

14. Spherical Mirrors – form a section of a sphere Convex – reflection on outer surface of sphere Concave – reflection on inner surface of sphere 23.3

15. 23.3 Formation of Images by Spherical Mirrors Terms Principal Axis – straight line normal to the center of the curve Focus – point where parallel rays intersect Vertex – center of the mirror Focal Length – distance from vertex to focus Images from distant objects are produced at the focal point 23.3

16. S-96 Sketch the path of a ray of light coming from an object in front a curved mirror to the eyes of an observer.

17. 23.3 Formation of Images by Spherical Mirrors The focal point is actually an approximation The greater the curve of a mirror, the worse is the approximation Called Spherical Aberration Examples of Visual Aberrations 23.3

18. 23.3 Formation of Images by Spherical Mirrors All rays follow the law of reflection Two Rules 1.A ray parallel to the principle axis reflects through the focal point 2.A ray through the focal point reflects parallel Examples of Diagrams – Concave Mirrors Real Images Virtual Image 23.3

19. S-98 Sketch a ray diagram for an object that is 10 cm from a concave mirror with a focal length of 12 cm. The object is 2 cm tall. Use a ruler.

20. S-99 Sketch a ray diagram for an object that is 5 cm from a concave mirror with a focal length of 3 cm. The object is 2.5 cm tall. Use a ruler.

21. 23.3 Formation of Images by Spherical Mirrors Convex Mirrors only form virtual images Rules 1.Rays parallel to the principle axis reflect away from the focal point 2.Rays headed for the focal point reflect parallel 23.3

22. 23.3 Formation of Images by Spherical Mirrors Curved Mirror Equations h o -object height h i -image height d o -object distance d i -image distance The Mirror Equation Magnification 23.3

23. 23.3 Formation of Images by Spherical Mirrors Sign Conventions Image Height + upright (virtual) - inverted (real) Image and Object Distance + front of mirror - behind mirror Magnification + upright image - inverted image 23.3

24. 23.3 Formation of Images by Spherical Mirrors Sign Conventions Focal Length + concave mirror - convex mirror 23.3

25. S-101 A 14 cm tall man, who apparently had a rough evening, stands 25 cm from a curved mirror with a focal length of 20 cm. a.What is the location of his image? b.What is the height of the image? c.What is the magnification of the image?

26. S-102 A 20 cm arrow is placed 25 cm from a concave mirror with a focal length of 15 cm. A.What is the position of the image? B.What is the height of the image? C.What is the magnification? D.Is the image real or virtual? E.Is it inverted or right side up? F.Is it enlarged or reduced?

27. Geometric Optics 23.4 Index of Refraction

28. Index of Refraction – the ratio of the speed of light in a vacuum to the speed in a given material 23.4 MaterialIndexMaterialIndex Vacuum1.00000NaCl1.54 Air at STP1.00029Polystyrene1.57 Water1.33Flint Glass1.65 Quartz1.46Sapphire1.77 Crown Glass1.53Diamond2.417

29. 23.4 Index of Refraction Value can never be less than 1 23.4 MaterialIndexMaterialIndex Vacuum1.00000NaCl1.54 Air at STP1.00029Polystyrene1.57 Water1.33Flint Glass1.65 Quartz1.46Sapphire1.77 Crown Glass1.53Diamond2.417

30. Geometric Optics 23.5 Refraction: Snell’s Law

31. Refraction – when a ray of light changes direction as it changes media The change in angle depends on the change in velocity of light (or the index of refraction of the two media) 23.5

32. 23.5 Refraction: Snell’s Law Snell’s Law – relates the index of refractions and the angles Also called the Law of Refraction If light speeds up, rays bend away from the normal If light slows down, rays bend toward the normal 23.5

33. 23.5 Refraction: Snell’s Law Refraction occurs when one side of the wave slows down before the other 23.5

34. Geometric Optics 23.6 Total Internal Reflection; Fiber Optics

35. When light travels from a more optically dense medium, the ray bends away from the normal As the angle increases, the angle of refraction eventually reaches 90 o. This is called the critical angle 23.6

36. S-100 A short, 1.5 m tall moose stands 1.4 m from a convex mirror with a focal length of 1.8 m. A.What is the location of the image? B.What is the height of the image? C.Describe the image. Repeat all steps for the mirror if it was concave.

37. S-104 A ray of light traveling from air into glass (n=1.68). A.Is there a critical angle? If so, what is it? B.What is the angle of refraction if the angle of incidence is 37 o ?

38. 23.6 Total Internal Reflection; Fiber Optics Above the critical angle, light reflects following the law of reflection Used in fiber optics 23.6

39. S-105 A.Light travels at 250,000,000 m/s through a piece of glass. What is its index of refraction? B.A mirror with a focal length of 25 cm forms an image that is -12.2 cm from the mirror. What is the distance of the object?

40. Geometric Optics 23.8 The Thin Lens Equation; Magnification

41. 23.8 The Thin Lens Equation: Magnification Equations are similar to Mirrors, conventions are different The Thin Lens Equation is To Calculate Magnification 23.8

42. 23.8 The Thin Lens Equation: Magnification Conventions Focal Length + converging lens - diverging lens Object Distance + same side as original light - different side (only when more than 1 lens) 23.8

43. 23.8 The Thin Lens Equation: Magnification Conventions Image Distance + opposite side from light - same side as light Height + upright - upside down 23.8

44. Geometric Optics 23.7 Thin Lenses; Ray Tracing

45. Thin lens – very thin compared to its diameter Diagrams are similar to mirrors Converging – rays converge 23.7

46. 23.7 Thin Lenses; Ray Tracing Converging Lenses 1.A ray parallel to the Principle Axis refracts through F 2.A ray through F’ refracts parallel. 3.A ray through the optical center, O, does not refract 23.7 Converging Lens

47. 23.7 Thin Lenses; Ray Tracing Diverging Lens – spreads apart rays of light Only produces virtual images Rules 1.Parallel rays refract away from F’ 2.Rays headed toward F refract parallel 3.Rays through O do not refract 23.7

48. S-106 Shortly before being released into the wild to fend for himself, a cute black bunny stands in front of a lens with a focal length of -24 cm. The bunny stands 32 cm in front of the lens. A.What is the location of the I mage? B.What is the height of the image? C.Describe the image.

49. S-105 A large refracting telescope is used to look at the image of stars in the night sky. The focal length of the lens is 450 m. A.What would be the location of the image? B.What would be the magnification?

50. Geometric Optics 23.9 Combinations of Lenses

51. Many devices used combinations of lenses Combination problems are treated as separate lenses Calculate or draw the image from the first lens 23.9 Applet