Chapter

1. Chapter Reflection and Mirrors

2. or Millions of light rays reflect from objects and enter our eyes – that’s how we see them! When we study the formation of images, we will isolate just a few useful rays: Web Link: Reflection, Refraction & Diffraction

3. measured fromthe normal A line  to the surface at the point of incidence i= r Law of reflection Reflection i = incident angle r = reflected angle

4. Ex: glossy vs. flat paint

5. Plane (flat) mirrors object mirror image Web Link: Plane mirror image To locate the image: 1) Draw 2 different rays leaving the same point. 2) Draw their reflections. 3) Extend the reflections behind the mirror. 4) The point where they meet locates the image.

6. Which type do you get from a plane mirror ? There are two different types of images: Real image Light rays actually meet at that point Virtual image Light rays only appear to emanate from that point For all plane mirrors: • Image is upright • Image is same size as object • object’s distance from mirror (do) = image’s distance from mirror (di) • Right and left are reversed

7. How tall a mirror do you need to be able to see your entire body? Does it matter how far away from the mirror you stand?

8. Multiple Reflections ( 2 or more mirrors) image object image image Web Link: Multiple reflections

9. Spherical Mirrors concave side convex side

10. Concave Spherical Mirrors principle axis (axis of symmetry) C R Parallel Rays (distant object): C F f f = ½ R Concave mirror C = Center of Curvature R = Radius of Curvature Web Link: Spherical mirrors and lenses F = focal point f = focal length Web Link: Concave Mirror

11. F Spherical Aberration Because of the spherical shape of the mirror, the outer rays don’t reflect through the focal point: This creates a blurry image Web Link: Spherical aberration Can you think of two ways that this problem could be eliminated? Web Link: Circular vs. parabolic mirror

12. Convex Spherical Mirrors C C R Parallel Rays (distant object): Since it’s behind the mirror F f f = -½ R Convex mirror Web Link: Spherical mirrors and lenses Web Link: Convex mirror

13. Ray #1: Parallel to the axis Relects through F Ray #2: Through F Reflects parallel to axis Ray #3: Through C Reflects back on itself Locating Images: Ray Tracing The use of 3 specific rays drawn from the top of the object to find location, size, and orientation of the image For a Concave Mirror:

17. Results: Ray Tracing for concave mirrors (in each case, draw in the 3 rays for practice) C C C Object is in front of C: Image is always real, smaller, and inverted Object between C and F: Image is always real, larger, and inverted F F F Object between F and mirror: Image is always virtual, larger and upright Ex: Makeup mirror

18. For a Convex Mirror: Ray #1: Parallel to the axis / Relects as if it came from F Ray #2: Heads toward F / Reflects parallel to axis Ray #3: Heads toward C / Reflects back on itself

19. C Wherever the object is: Image is always virtual, smaller and upright Ex: Car side mirrors • Convex mirrors widen the field of view • “Objects in mirror are closer than they appear” F Results: Ray Tracing for convex mirrors (draw in the 3 rays for practice) Web Link: Ray tracing

20. The Mirror Equation works for both concave and convex mirrors: C C f f do do + for in front of mirror (real) F F - for behind mirror (virtual) The Mirror Equation OR f = mirror’s focal length (+ for concave, - for convex ) do = distance between object and mirror di = distance between image and mirror

21. The Magnification Equation m is + if the image is upright m is - if the image is inverted m>1 if the image is larger than object m<1 if the image is smaller than object What about the size of the image ?? ho = height of object hi = height of image m = magnification = hi /ho

22. Ex: 15 cm 80 cm The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the cat.

23. Ex: 15 cm 80 cm The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the dog.

24. Chapter Refraction and Lenses

25. air glass air light slows down (v<c) Refraction- the bending of a light ray as it passes from one medium to another Web Links: Photon in medium & vacuum, Marching band, Refraction

26. Notes: varies for different media varies for different media stays the same c = speed of light in a vacuum v = speed of light in a particular medium • For any medium, n > 1 • v = f Web Link: Refractive index

27. Ex: If the speed of light in glass is 1.97 x 108 m/s, calculate the index of refraction for glass.

28. Don’t forget to measure angles from The Normal n1 = initial medium n2 = final medium 1 = incident angle 2 = refracted angle

29. n1 sin 1 = n2 sin 2 Snell’s Law Notice: If n2>n1 : lightray bends toward the normal If n2<n1 :lightray bends away from the normal

30. Ex: air 60 water Find both the angle of reflection and the angle of refraction for this light ray incident upon water.

31. Critical Angle Diamonds Fiber Optics Total Internal Reflection Web Link: Total internal reflection Examples:

32. Ex: Find the critical angle for light traveling from water toward air.

33. This makes spearfishing very difficult! Apparent Depth When viewed from another medium, objects appear to have a different depth than they actually do.

34. When viewed from directly above: n1 = medium containing object n2 = medium containing observer d= apparent depth d = actual depth

35. Example of Apparent Depth:

36. Ex: 11 cm How far above the water does the cat look to the fish?

37. Red: longest  lowest n Violet: shortest  highest n bends the most Dispersion Index of refraction (n) depends slightly on wavelength () Web Link: Prism

38. Rainbows are a result of dispersion

39. Sometimes a double rainbow can be seen. This is caused by a second internal reflection.

40. f Converging Lens Diverging Lens F F f Lenses

41. Find the focal length of a converging lens by holding it up to a window. (See how far away from the lens you need to hold a piece of paper to focus the image on the paper.) Web Link: Spherical mirrors and lenses

42. Ray Tracing for Lenses Ray #1: Parallel to the axis Refracts through F Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected • Light passes through a lens • There is a focal point on both sides of a lens Converging Lens:

43. Example: Camera

44. Example: Slide Projector

45. Example: Magnifying Glass Web Link: Ray tracing

46. Results: Ray Tracing for Converging Lenses (in each case, draw in the 3 rays for practice) Object distance > 2f: Image is real, smaller, and inverted Object between f and 2f: Image is real, larger, inverted F F 2F F F 2F F F 2F Object between f and lens: Image virtual, larger, upright

47. For a Diverging Lens: Now, for Diverging lenses…… Web Link: Spherical mirrors and lenses Ray #1: Parallel to the axis on the left Refracts as if it came from F on the left Ray #2: Heads toward F on the right Refracts parallel to the axis on the right Ray #3: Through the center of the lens undeflected

48. Example: Glasses to correct nearsightedness 2

49. F F Web Link: Ray Tracing Summary for Mirrors and Lenses Results: Ray Tracing for Diverging Lenses (draw in the 3 rays for practice) No matter where the object is: Image is always virtual, smaller and upright Web Link: Ray tracing

50. But the variables are defined slightly differently now because………. For a lens, a real image is on the opposite side as the object For a mirror, a real image was on the same side as the object These equations also work on lenses: The Thin Lens Equation The Magnification Equation