1. Mirrors and Images

2. Light Review A luminous object emits light (ex: the sun) An illuminated object reflects light (ex: the moon) For both, light emits/reflects in a variety of directions. Your eye only sees the very small cone of rays that is coming towards it.

3. Image Formation For an image to form, light must be reflected back to the eye. When you look at an object, the light is reflected back along a line of sight. Light travels in straight lines.

4. Law of Reflection When a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. (Ɵ i = Ɵ r ) Incident Ray (I) – ray of light approaching the mirror Reflected Ray (R) – ray of light reflecting off the mirror Normal line (N) – a line drawn perpendicular to the surface of the mirror at the point of incidence. Angle of incidence (Ɵ i ) – between I and N Angle of reflection (Ɵ r ) – between R and N

5. Law of Reflection The law of reflection applies to both smooth and rough surfaces Specular (planar) reflection occurs when light reflects off a smooth surface. Ex: mirrors, calm bodies of water

6. Law of Reflection Diffuse reflection occurs when light reflects off a rough surface. Ex: asphalt, paper, clothing

7. Three types of Mirrors Plane mirror – flat and smooth Concave mirror - caved in, silvered on the inside of the sphere Convex mirror – pushed out, silvered on the outside of the sphere

8. Plane Mirrors When you look into mirror: you are the object and what you see is the image The image location is the one location in space where it seems to every observer that the light is diverging(coming) from. Light reflects off an object in multiple directions

9. Plane Mirrors Some light reaches the mirror and reflects off the mirror (law of reflection) Each reflected ray can be extended backwards behind the mirror The point where these ray extensions meet is the image

10. Image Formation

11. Plane Mirror Image Characteristics Images formed by plane mirrors are called virtual Virtual images are images that form in locations where light does not actually reach, but only appears to reach Virtual images form behind the mirror

12. Plane Mirror Image Characteristics Virtual images are reversed left to right Virtual images are upright The image distance (d i ) is the same as the object distance (d o ) Virtual images are the same size (nonmagnified) as the object.

13. Concept Check 1.Reflection in which light rays are all reflected in the same direction (parallel) is called: A. Diffuse reflection B.Specular reflection 2.A __________________ is a flat, smooth surface A. Concave mirror B. Convex mirror C. Plane mirror

14. Concept Check 3. A plane mirror produces an image that is ____________ than the actual object. A. Larger than B. Smaller than C.The same size as 4.The images produced by plane mirrors are ______________. A. Virtual images B. Real images

15. Concept Check 5. Where is the image located that is produced by a plane mirror? A.In front of the mirror B.On the surface of the mirror C.Behind the mirror

16. Mirrors Like a portion of a sphere that was sliced away and then silvered on one of the sides to form a reflecting surface. Concave or Convex

17. Spherical Mirrors Concave mirrors are the inside portions of a spherical mirror The reflective side is inside

18. Anatomy of a curved mirror Principal axis – A line passing through the center of the sphere and attaching to the mirror in the exact center Center of Curvature (C) – The point in the center of the sphere from which the mirror was sliced. Vertex (A) – The point on the mirror’s surface where the principal axis meets the mirror. The geometric center of the mirror.

19. Anatomy of a curved mirror Focal point (F) – Midway between the vertex and the center of curvature Radius (R) – Distance from the vertex to the center of curvature. Focal length (f) – Distance from the mirror to the focal point. Equal to half the radius.

20. Concave Mirrors The normal line extends through the center of curvature Once the normal is found, angles of incidence and reflection can be calculated to determine the image location (where the reflected rays meet)

21. Real vs Virtual images Concave mirrors are capable of producing real and virtual images An image is real if the rays converge A real image can be seen on a piece of paper or projected on a screen Real images are inverted and form in front of the mirror Real images can be smaller, larger, or the same size as the object The size of the real image depends on where the object is located in reference to the focal point

22. Concave mirror The two rules of reflection for concave mirrors are: Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.the principal axisfocal point Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.focal pointthe principal axis

23. Ray Diagrams for Concave Mirrors Steps: Draw the mirror and the principal axis. Label the focal point and center of curvature. Draw the object. Draw 3 rays to locate the image. The image forms where the reflected rays meet.

24. Ray Diagrams for Concave Mirrors Step 1: From the top of the object, draw 2 incident rays traveling towards the mirror – one passing through the focal point and one traveling parallel to the principal axis. Use arrows to indicate direction of incident rays.

25. Ray Diagrams for Concave Mirrors Step 2: Reflect the rays according to the two rules. Ray passing through the focal point to the mirror will reflect and travel parallel to the principal axis. Ray traveling parallel to the principal axis on the way to the mirror will reflect and travel through the focal point. Use arrows to indicate direction.

26. Ray Diagrams for Concave Mirrors Step 3: Mark the top of the image. Draw a straight line from the top of the image to the principal axis. The image point is where the 2 reflected rays intersect.

27. Image Characteristics: LOST The goal of drawing Ray diagrams is to find the following: L: What is the image location? O: What is the image orientation? (upright or inverted) S: What is the image size? (larger, smaller or same size as object) T: What is the image type? (real or virtual)

28. 5 Cases (Scenarios) of Concave Mirrors Depends on location of the object – will result in different images Case 1: the object is located beyond the center of curvature (C) Case 2: the object is located at the center of curvature (C) Case 3: the object is located between the center of curvature (C) and the focal point (F) Case 4: the object is located at the focal point (F) Case 5: the object is located in front of the focal point (F)

29. 5 Cases of Concave Mirrors

30. Case 1: Object is located beyond C

31. Case II: Object is located at C

32. Case III: Object is located between C and F

33. Case IV: Object is located at F No Image is Formed Why? Light rays neither converge/diverge after reflecting off mirror

34. Case V: Object is located in front of F

35. Concave mirror summary: Case #Object LocationImage locationOrientationSizeType 1Beyond C Between C & FInvertedReducedReal 2At C Inverted Same size Real 3Between C and F Beyond C Inverted Larger Real 4At F No Image 5In front of F Behind mirrorUprightLarger Virtual

36. Convex Mirrors A convex mirror is a portion of a sphere that had been sliced away and the outside of the sphere is silvered so that it can reflect light. There are the same components (C, F, principal axis) but they are located on the side of the mirror opposite the object - behind the mirror. Since the focal point is located behind the mirror, it is said to have a negative focal length value

37. Convex Mirrors A convex mirror is sometimes called a diverging mirror because incident light will reflect off the mirror and diverge (does not come together at a central point) Since they will never intersect on the object side of the mirror, all convex mirrors produce virtual images that are located somewhere behind the mirror.

38. Convex mirror rules: Any incident ray traveling parallel to the principal axis will reflect so that its extension will pass through the focal point.the principal axisfocal point Any incident ray traveling so that its extension passes through the focal point will reflect and travel parallel to the principal axis.focal pointthe principal axis

39. Drawing convex mirrors Same steps are followed as for concave mirrors, except the reflected rays are extended backwards across the mirror to the other side to a point of intersection. This point is the image location of the object.

40. Convex mirrors So the image of an object in front of a convex mirror will ALWAYS be located at a position behind the convex mirror. The image will ALWAYS be upright, reduced in size (smaller than the object), and virtual.

41. Convex mirrors Another characteristic of images formed by convex mirrors is as the object distance is decreased, the image distance is decreased and the image size is increased.

42. Mirror Math The mirror equation expresses the quantitative relationship between the: object distance (d o ) image distance (d i ) focal length (f)

43. Mirror math The magnification equation expresses the quantitative relationship between the: object distance (d o ) image distance (d i ) focal length (f) object height (h o ) image height (h i )

44. Example 1: You are standing in front of a Fun house mirror that makes you very small. If you are standing 1.4 meters from the mirror and your image appears 1.2 meters behind the mirror, what is the focal length?

45. Example 1 Answer f = ? d o = 1.4 m d i = 1.2 m 1 = 1 + 1 f 1.4 1.2 1 = 0.67 + 0.83so 1/f = 1.5, so f = 0.65 f

46. Example 2: A 4.0 cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and image size.

47. Example 2 Answer h o = 4.0 cmd o = 45.7 cm f = 15.2 cm d i = ? h i = ? Use the mirror eq to find d i, then use the magnification eq to find h i : 1 = 1 + 1 15.2 45.7 d i 0.0658 = 0.0219 + 1/d i 0.0658 – 0.0219 = 0.0439 0.0439 = 1/d i d i = 22.8 cm

48. Example 2 Answer h i = -22.8 4.0 45.7 h i = -1.99 cm The negative value for image height indicates the image is inverted.

49. Example 2 Answer Which case does this example represent? The image is inverted and smaller so it must be case ___________

50. Example 3: A 4.0 cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and image size.

51. Sign Conventions f is + = if mirror is concave f is - = if mirror is convex d i is + = if image is real (located on object’s side of mirror) d i is - = if image is virtual (located behind the mirror) h i is + = if image is upright (therefore virtual) h i is - = if image is inverted (therefore real)