1. 14-3: Curved Mirrors

2. Curved Mirrors
What are some examples of curved mirrors?

3. Concave Spherical Mirrors
A spherical mirror has the shape of part of a sphere’s surface.
Concave Spherical Mirror (Converging Mirror): A spherical mirror with light reflecting from its silvered, concave surface
Concave mirrors are used whenever a magnified image of an object is needed

4. Terms you need to know Term Definition Symbol(s) Center of Curvature
The center of the spherical shell of which the mirror is a small part C
Radius of Curvature
The distance from the mirror’s surface to the center of curvature R
Height of object
The height of the object
h; ho
Height of image
The height of the image
h’, hi
Object distance
The distance between the object and the mirror
p; do
Image distance
The distance between the image and the mirror
q; di
Focal Length
Focal length is equal to half the radius of curvature f

5. Concave Spherical Mirrors (p.531)
Object
Principal Axis C f
A spherical mirror is represented as a shell of a sphere

6. Concave Mirror (p.531)

7. The Mirror Equation
To use the mirror equation, you must use the correct signs.
Object and image distances are positive if they form on the front side of the mirror
Object and image distances are negative if they form on the back side of the mirror

8. Sample Problem (p.536 #2)
A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm.

9. Solve the problem
p = .93 m
f = .33 m
q=?

10. Magnification Equation

11. Sample Problem (p.536 #2)
A concave shaving mirror has a focal length of 33 cm. Calculate the magnification of the image. Is the image real or virtual? Is the image inverted or upright?

12. Sign Conventions for Magnification
Orientation of image with respect to object
Sign of M
Type of image
Upright +
Virtual
Inverted -
Real

13. Find the magnification
The magnification is negative, therefore the image is real and inverted.

14. Ray Diagrams
A ray diagram is a drawing that uses geometry to locate an image formed by a mirror.
There are different rules for drawing ray diagrams depending on the type of mirror you have.

15. How to draw a ray diagram (p. 533-534)
For spherical mirrors, there are three different reference rays.
The intersection of any two rays locates the image

16. Rules for drawing reference rays (p. 534)
Line drawn from object to mirror
Line drawn from mirror to image after reflection 1
Parallel to principal axis
Through focal point F 2 3
Through center of curvature (C)
Back along itself through C

17. How to draw a ray diagramf C
Ray 1
Ray 3
Ray 2
The intersection
Of any 2 rays gives the image location

18. Objects inside the focal point

19. Sample Problem (p.536 #2)
A concave shaving mirror has a focal length of 33 cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. Draw a ray diagram to confirm your results.

20. Draw the diagram f C
The image is inverted and about half the height of the object.

21. Convex Mirrors
Convex mirrors take objects in a large field of view and produce a small image
Side-view mirrors on cars are convex mirrors. That’s why they say “objects are closer than they appear”

22. Convex Spherical Mirrors (p. 537)
A convex spherical mirror (diverging mirror) is silvered so that light is reflected from the sphere’s outer, convex surface
The image distance is always negative!
The image is always a virtual image!
The focal length is negative !

23. Ray diagrams for convex mirrors
The focal point and center of curvature are behind the mirror’s surface
A virtual, upright image is formed behind the mirror
The magnification is always less than 1 f C

24. Drawing the reference rays
Ray 1 is drawn parallel to the principal axis beginning at the top of the object. It reflects from the mirror along a line that intersects the focal point f C

25. Ray 2
Ray 2 starts from the top of the object and goes as though its going to intersect the focal point but it reflects parallel to the principal axis
Ray 1
Ray 2 f C

26. Ray 3
Ray 3 starts at the top of the object and goes as though its going to intersect the center of curvature
Ray 1
Ray 3
Ray 2 f C

27. Convex Spherical Image Formation
The image forms at the intersection of any two of the three rays behind the mirror.
Ray 1
Ray 3
Ray 2 f C
The rays do not intersect in front of the mirror!!

28. Sign conventions for mirrors (p. 538)

29. Sample Problem (p. 540 #6)
A candle is 49 cm in front of a convex spherical mirror that has a focal length of 35 cm. What are the image distance and magnification? Is the image virtual or real? Is the image inverted or upright? Draw a ray diagram to confirm your results.

30. Solving the problem
Remember that for convex mirrors, the focal length and image distance are always negative.

31. The Magnification of the Image
Since the magnification is positive, the image is upright and virtual

32. Ray diagram for the ImageC f
Remember that you only need to draw two of the three rays to find the image.