The document summarizes key concepts about the reflection of light by plane and spherical mirrors, including: 1) Plane mirrors form virtual, upright images that are the same size as the object and located the same distance behind the mirror as the object is in front of it. 2) Spherical mirrors can form real or virtual images, depending on whether the mirror is convex or concave. Concave mirrors always form virtual images while convex mirrors form real images. 3) Ray diagrams can be used to locate the image position by tracing the path of light rays reflecting off the mirror according to the law of reflection.

1. Chapter 25 The Reflection of Light: Mirrors

2. AP Learning Objectives Geometric Optics Reflection Students should understand the principles of reflection and refraction, so they can: Show on a diagram the directions of reflected rays.

3. AP Learning Objectives Mirrors Students should understand image formation by plane or spherical mirrors, so they can: Locate by ray tracing the image of an object formed by a plane mirror, and determine whether the image is real or virtual, upright or inverted, enlarged or reduced in size. Relate the focal point of a spherical mirror to its center of curvature. Locate by ray tracing the image of a real object, given a diagram of a mirror with the focal point shown, and determine whether the image is real or virtual, upright or inverted, enlarged or reduced in size. Use the mirror equation to relate the object distance, image distance, and focal length for a lens, and determine the image size in terms of the object size.

4. Table Of Contents Wave Fronts and Rays The Reflection of Light The Formation of Images by a Plane Mirror Spherical Mirrors The Formation of Images by Spherical Mirrors The Mirror Equation and the Magnification Equation

5. Chapter 25: The Reflection of Light: Mirrors Section 1: Wave Fronts and Rays

6. Parts of a wave Before we discuss optics… Let’s discuss two important ways to describe the propagation of a wave Wave Fronts Line connecting all adjacent point that are in the same phase Imagine drawing a line across the top of a wave crest Rays The radial lines starting from the source of the wave, tracing the path of the wave Shows the direction of propagation

7. Wave Fronts & Rays A hemispherical view of a sound wave emitted by a pulsating sphere. The rays are perpendicular to the wave fronts.

8. Wave Fronts & Waves At large distances from the source, the wave fronts become less and less curved.

9. Chapter 25: The Reflection of Light: Mirrors Section 2: The Reflection of Light

10. Boundary Effects Back in Chapter 16 we discussed two important effects a boundary can have on a wave Reflection Topic for this chapter Occurs when a wave strikes a medium boundary and “bounces back” into the original medium Refraction will be discussed in chapter 26 Transmission of wave from one medium to the next.

11. The Law of Reflection The incident ray, the reflected ray, and the normal to the surface all lie in the same plane, and the angle of incidence equals the angle of reflection.

12. Types of Reflection In specular reflection, the reflected rays are parallel to each other. Occurs when rays strike “shiny” surface In Diffuse reflection, the reflected rays scatter Occurs when rays strike a “rough” surface

13. 25.2.1. You are talking with a friend in a closed room that has no windows, no objects, and no furniture. The only thing in the room is an overhead incandescent light that is turned on. You are looking at your friend and begin thinking about whether you are seeing your friend as a result of reflection. Does reflection play a role in seeing your friend? a) No, the room is just illuminated by the overhead light. b) No, visible light is emitted by my friend and enters my eye. c) Yes, the visible light from the overhead light bulb is specularly reflected from my friend and enters my eye. d) Yes, the visible light from the overhead light bulb is diffusely reflected from my friend and enters my eye.

14. 25.2.2. You are in a closed room that has no windows and only one source of light, an overhead incandescent light bulb. Around the room, you notice various objects: a yellow banana, a red apple, and a green cucumber. Which of the following best explains what influences the color and brightness of the banana? a) Color is a property of each object, independent of any light shining on it. The brightness is only dependent on the brightness of the light bulb. b) Some of the white light is absorbed by the banana, but the portion of the spectrum that is yellow is reflected from the banana. The brightness also depends on the roughness of the surface of the banana. c) Color is a property of each object, independent of any light shining on it. The brightness is only dependent on the roughness of the surface of the banana. d) Some of the white light is absorbed by the banana, but the portion of the spectrum that is yellow is reflected from the banana. The brightness is only dependent on the brightness of the light bulb. e) The banana only emits light that has wavelengths in the yellow light portion of the visible light spectrum. The brightness is only dependent on the brightness of the light bulb.

15. 25.2.3. You are standing on the right side of a closed opaque box. There is a hole through which you can look inside. The drawing shows a small light bulb inside that is on. There is also a wall inside the box as shown. All of the surfaces of the box are rough surfaces that are painted black. As you look through the hole, what can you see? a) a bright beam of light from the bulb b) the light bulb c) the walls will appear to be the same color as the light bulb d) the black walls of the box e) nothing

16. Chapter 25: The Reflection of Light: Mirrors Section 3: The Formation of Images by a Plane Mirror

17. What is an image? For you to see an object, light must be emitted from it or reflected off of it towards your eye. An image is a reflection of light such that light appears to leave that imaginary location in space. One common object that creates an image is a mirror.

18. Ray Tracing Ray tracing is a method of constructing an image using the model of light as a ray. We use ray tracing to construct optical images produced by mirrors and lenses. Ray tracing lets us describe what happens to the light as it interacts with a medium.

19. Ray Diagrams for Flat Mirror Draw the “object” and the mirror Draw a ray from the object towards the mirror Ray reflects according to the law of reflection Extend the reflected ray behind the mirror Repeat process for a second ray from the object Where the two lines intersect is location of image

20. Ray Diagrams A ray of light from the top of the chess piece reflects from the mirror. To the eye, the ray seems to come from behind the mirror. Because none of the rays actually emanate from the image, it is called a virtual image.

21. Image Distance = Object Distance The geometry used to show that the image distance is equal to the object distance.

22. The person’s right hand becomes the image’s left hand. The image has three properties: It is upright. It is the same size as you are. The image is as far behind the mirror are you are in front of it. The Formation of an Image in a Plane Mirror

23. Optical Images With other optical devices, there are other possible images: Nature: Real (converging) Virtual (diverging) Orientation Upright Inverted Size True Enlarged Reduced

24. Conceptual Example 1 Full-Length Versus Half-Length Mirrors What is the minimum mirror height necessary for her to see her full image?

25. 25.3.1. The word “ME” is printed in bold letters on a transparent plastic sheet. It is then held up in front of a plane mirror as shown. How will the word appear in the mirror when you look at its image?

26. 25.3.2. You are standing in front of a mirror at the point P shown. There is a light bulb behind a screen that you cannot see directly. As you look in the mirror, where does the image of the light bulb appear? a) A b) B c) C d) D e) E

27. 25.3.3. A supermodel walks directly toward a plane mirror at a speed of 0.15 m/s. Determine the speed of the image relative to her . a) 0.15 m/s b) 0.30 m/s c) 0.45 m/s d) 0.60 m/s e) 0.90 m/s

28. Chapter 25: The Reflection of Light: Mirrors Section 4: Spherical Mirrors

29. If the inside surface of the spherical mirror is polished, it is a concave mirror. If the outside surface is polished, is it a convex mirror. The law of reflection applies, just as it does for a plane mirror. Spherical Mirrors

30. Important parts of Ray Diagrams The principal axis of the mirror is a straight line drawn through the center and the midpoint of the mirror. The focal point is ½ the distance from the mirror to the center of curvature. Positive if light can pass through it Negative if light cannot pass through it.

31. How to find the focal point Incident rays that are near to and parallel to the Principal Axis will bend through the focal point. The focal length is the distance between the focal point and the mirror.

32. Spherical Aberration Rays that lie close to the principal axis are called paraxial rays. Rays that are far from the principal axis do not converge to a single point. The fact that a spherical mirror does not bring all parallel rays to a single point is known as spherical aberation. Can be corrected with Parabolic Mirrors

33. Convex Mirrors When paraxial light rays that are parallel to the principal axis strike a convex mirror the rays appear to originate from the focal point.

34. Chapter 25: The Reflection of Light: Mirrors Section 5: The Formation of Images by Spherical Mirrors

35. Making Ray Diagrams Must draw two of the following three sets of lines: the p-ray, which travels parallel to the principal axis, then reflects “through focus”. the f-ray, which travels “through focus”, then reflects back parallel to the principal axis. the c-ray, which travels “through center”, then reflects back “through center.” C f

36. Convex Ray Diagram Where’s the image? Where all three reflected lines intersect C f

37. 25.5.1. Which one of the following statements concerning a convex mirror is true? a) Such mirrors are always a portion of a large sphere. b) The image formed by the mirror is sometimes a real image. c) The image will be larger than one produced by a plane mirror in its place. d) The image will be closer to the mirror than one produced by a plane mirror in its place. e) The image will always be inverted relative to the object.

38. 25.5.2. Imagine you are sitting in the back row of the classroom. Your instructor is standing in the front of the room with a large convex spherical mirror. What do you see in the mirror as your instructor walks from the front of the room to your location; all the while the mirror is facing you? a) I see my image right side up. It gets larger as the mirror approaches. b) I see my image right side up. It gets smaller as the mirror approaches. c) I see my image initially inverted and then right side up. It gets larger as the mirror approaches. d) I see my image initially inverted and then right side up. It gets smaller as the mirror approaches. e) I see my image initially right side up and then inverted. It gets larger as the mirror approaches.

39. 25.5.3. Imagine you are sitting in the back row of the classroom. Your instructor is standing in the front of the room with a large concave spherical mirror. What do you see in the mirror as your instructor walks from the front of the room to your location; all the while the mirror is facing you? a) I see my image right side up. It gets larger as the mirror approaches. b) I see my image right side up. It gets smaller as the mirror approaches. c) I see my image initially inverted and then right side up. It gets larger as the mirror approaches. d) I see my image initially inverted and then right side up. It gets smaller as the mirror approaches. e) I see my image initially right side up and then inverted. It gets larger as the mirror approaches.

40. 25.5.4. An object is placed at the center of curvature of a concave spherical mirror. Which of the following descriptions best describes the image produced in this situation? a) upright, larger, real b) inverted, same size, real c) upright, larger, virtual d) inverted, smaller, real e) inverted, larger, virtual

41. 25.5.5. An object is placed to the right of a spherical mirror that is concave towards the object. The object is at the focal point of the mirror. Which one of the following is the best description of the image? a) The image is to the left of the mirror and it is larger than the object. b) The image is to the left of the mirror and it is smaller than the object. c) The image is to the right of the mirror and it is larger than the object. d) The image is to the right of the mirror and it is smaller than the object. e) No image is formed in this situation.

42. 25.5.6. Which of the following best describes the type of image formed when an object is placed between a concave mirror and its focal point? a) real b) virtual c) No image is formed in this case.

43. 25.5.7. Which of the following best describes the type of image formed when an object is placed at a distance greater than the focal point of a concave mirror? a) real b) virtual c) No image is formed in this case.

44. 25.5.8. Which of the following best describes the type of image formed when an object is placed between a convex mirror and its focal point? a) real b) virtual c) No image is formed in this case.

45. Chapter 25: The Reflection of Light: Mirrors Section 6: The Mirror Equation and the Magnification Equation

46. Optics Variables

47. Mirror Equations These diagrams are used to derive the mirror equation.

48. Sign Conventions for Spherical Mirrors

49. Summary of convention If the ray of light actually goes through the point in space The distance is positive If the line must be extended to show where it appears to travel The distance in negative If the image is in the same direction as the object The magnification is positive If opposite direction, The magnification is negative If m>1, the image size is enlarged If m<1, the image size is reduced If m=1, the images size is true

50. Example 5 A Virtual Image Formed by a Convex Mirror A convex mirror is used to reflect light from an object placed 66 cm in front of the mirror. The focal length of the mirror is -46 cm. Find the location of the image and the magnification.

51. 25.6.1. An object is placed to the right of a spherical mirror that is concave towards the object. The focal length of the mirror is 12 cm. If the object is located 8 cm from the mirror, what is the image distance? a)  8 cm b) +12 cm c)  12 cm d)  24 cm e) +24 cm

52. 25.6.2. While shopping in a grocery store you look up at a convex security mirror. You notice that your image is about one-fourth of your height. By estimating your distance to be 2.0 meters in front of the mirror, determine the focal length of the mirror. a) 0.67 m b) 1.3 m c) 2.0 m d) 4.0 m e) 6.0 m

53. 25.6.3. Consider the strange device placed at the center of curvature of a concave spherical mirror shown in the drawing. The focal length of the mirror is 5.0 cm. The device has two light bulbs, but the lower one happens to be burned out. What will happen when the upper light bulb is turned on? a) The lit bulb’s image will appear inverted at the same distance behind the mirror, but the image of the unlit bulb will not be seen. b) The lit bulb’s image will appear inverted at the same distance behind the mirror and the image of the unlit bulb will be seen as the upper bulb. c) The lit bulb’s image will appear inverted at the same location as the unlit bulb, so the unlit bulb will look like its turned on. d) The lit bulb’s image will appear inverted at the focal point and the image of the unlit bulb will be seen as the upper bulb. e) The lit bulb’s image will appear inverted at the at the focal point and the image of the unlit bulb will not be seen.

54. 25.6.4. In which of the following cases is the image virtual? a) It is on the same side of the mirror as the object. b) The image is virtual if you can only see it when projected onto a surface. c) The lateral magnification is negative. d) The distance from the mirror to the image is greater than the distance from the mirror to the object. e) None of the cases above produce a virtual image.

55. 25.6.5. In which of the following cases is the image real? a) It is on the opposite side of the mirror from the object. b) The image is real if you can project it onto a surface. c) The lateral magnification is positive. d) The image is upright (not inverted relative to the object). e) None of the cases above produce a real image.

56. 25.6.6. For a certain situation involving an object and a spherical mirror, the resulting lateral magnification is negative. Which of the following properties necessarily may be attributed to the image? a) real b) virtual c) oriented in the same direction as the object d) oriented in the opposite direction as the object e) No image can be produced when the lateral magnification is negative.

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