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

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

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

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

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

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

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

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

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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