1. Mirrors

2. Outline Vocabulary Law of Reflection Ray Diagrams
Images from a Concave Mirror
Virtual vs Real Mirrors
Mirror Equation

3. Vocabulary
Principal axis- a line passing through the center of a virtual sphere (on which the mirror sits) and the exact center of a mirror

4. Vocabulary
Center of Curvature- The point in the center of the sphere from which the mirror was sliced (C)

5. Vocabulary
Vertex- the point on the mirror’s surface where the principal axis meets the mirror (A)

6. Vocabulary
Focal Point- point half way between the vertex and the center of curvature (F)

7. Vocabulary
Radius of Curvature- distance from the vertex to the center of curvature (R)

8. Vocabulary
Focal Length- distance from the vertex to the focal point (f)

9. Law of Reflection
For a light ray reflected off the surface of any mirror, the angle of incidence equals the angle of reflection, where both angles are measured from the surface normal
𝜃 𝑖 = 𝜃 𝑟

10. Law of Reflection For a concave mirror:
Normal line extends from point of incidence to center of curvature
Angle of incidence is measured from this normal

11. Law of Reflection
Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.
Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

12. Law of Reflection For a convex mirror:
Normal line is perpendicular to a tangent line at point of incidence
Angle of incidence is measured from this normal

13. Ray Diagrams Incident rays connect object to mirror
Reflected rays obey the law of reflection
Angle of incidence = angle of reflection
Measured from normal at point of incidence
Image is produced at intersection of reflected rays

14. Drawing Ray Diagrams
Draw 2 rays from the top of the object to the mirror
One ray must run parallel to the radius of curvature
One ray must run from the object, through the focal point

15. Drawing Ray Diagrams Apply the law of reflection to each incident ray
Repeat, starting at bottom of object

16. Drawing Ray Diagrams

17. Images from Concave Mirrors
Case 1: Object is located beyond center of curvature
Image is inverted
Image is smaller than object
Image is located between C and F
Magnification is less than 1
Image is real

18. Images from Concave Mirrors
Case 2: Object is located at center of curvature
Image is inverted
Image is same size as object
Image is located at C
Magnification is 1
Image is real

19. Images from Concave Mirrors
Case 3: Object is located between center of curvature and focal point
Image is inverted
Image is larger than object
Image is located beyond C
Magnification is greater than 1
Image is real

20. Images from Concave Mirrors
Case 4: Object is located at focal point
No image is formed

21. Images from Concave Mirrors
Case 5: Object is located in front of focal point
Image is upright
Image is larger than object
Image is located beyond mirror
Magnification is greater than 1
Image is virtual

22. Virtual vs. Real Images
Virtual Images
Real Images
Formed in locations where light does not actually reach
Light only appears to emanate from that location
A surface placed at the image location will not show the image
Image is located beyond mirror
Light does actually converge
A surface placed at the convergence location will show the image

23. Mirror Equation
1 𝑓 = 1 𝑑 𝑜 + 1 𝑑 𝑖 f = focal length do = distance between mirror and object di = distance between mirror and image

24. Magnification Ratio of height of image to height of object 𝑀= ℎ 𝑖 ℎ 0
𝑀= ℎ 𝑖 ℎ 0
𝑀=− 𝑑 𝑖 𝑑 𝑜

25. Sign Conventions for Mirror Equations
Variable
Positive
Negative f
Concave mirror
Convex mirror di
Real image, located on object’s side of mirror
Virtual image, located behind mirror hi
Upright image, virtual
Inverted image, real

26. Clicker Question 1
A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. What is the image distance?
15.18 cm
22.73 cm
30.51 cm
45.73 cm B

27. Clicker Question 2
A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. What is the image height?
5.98 cm
4.00 cm
8.03 cm
12.03 cm A

28. Clicker Question 3
A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Will the image be upright or inverted?
Upright
Inverted B

29. Clicker Question 4
A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Is the image real or virtual?
Real
Virtual A

30. Clicker Question 5
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. What is the image distance? cm
-0.14 cm
0.14 cm
18.28 cm
(NOTE: this is the same object and the same mirror, only this time the object is placed closer to the mirror.) D

31. Clicker Question 6
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. What is the image height?
2.31 cm
6.9 cm
8.81 cm
60.8 cm C

32. Clicker Question 7
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. Is the image upright or inverted?
Upright
Inverted A

33. Clicker Question 8
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. Is the image real or virtual?
Real
Virtual B

34. Practice Problem 1
A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?

35. Practice Problem 2
Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.

36. Practice Problem 3
The infamous Chinese magician Foo Ling Yu places a 56-mm tall light bulb a distance of 124 cm from a spherical concave mirror with a focal length of 62 cm.

37. Practice Problem 4
In a physics demonstration, a concave mirror having a 50.0 cm focal length is used to create images of a candle located at various locations along its principal axis. Beginning from a distance of several meters from the mirror, a candle is moved forward and its image is projected onto an opaque screen. Determine the image distances (distance from mirror to image) for object distances (distance from object to mirror) of … a. … cm b. … cm c. … 75.0 cm d. … 50.0 cm (Be careful with your math; the result is surprising.) e. … 25.0 cm