14-3: Curved Mirrors
Curved Mirrors
• What are some examples of curved mirrors?
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
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
Concave Spherical Mirrors (p.531)
Object
Principal Axis
C
f
A spherical mirror is represented as a shell of a sphere
Concave Mirror (p.531)
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
1 1 1
 
p q f
1
1
1


object distance image distance focal length
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.
Solve the problem
1 1 1
 
p q f
• p = .93 m
• f = .33 m
• q=?
1 1 1
1
1
  

 .01955
q f p .33m .93m
q  .51 m  51.15cm
Magnification Equation
hi
q
M 

ho
p
image height
image distance
Magnificati on  

object height
object distance
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?
Sign Conventions for Magnification
Orientation of
Sign of M
image with
respect to object
Upright
Inverted
Type of image
+
Virtual
-
Real
Find the magnification
hi
q
.51
M 
 
 .55
ho
p
.93
The magnification is negative, therefore the
image is real and inverted.
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.
How to draw a ray diagram (p. 533534)
• For spherical mirrors, there are three different
reference rays.
• The intersection of any two rays locates the
image
Rules for drawing reference rays (p.
534)
Ray
Line drawn from object to mirror
Line drawn from
mirror to image
after reflection
1
Parallel to principal axis
Through focal
point F
2
Through focal point F
Parallel to
principal axis
3
Through center of curvature
(C)
Back along itself
through C
How to draw a ray diagram
Ray 1
Ray 2
C
The intersection
Of any 2 rays gives the
image location
f
Ray 3
Objects inside the focal point
C
f
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.
Draw the diagram
C
The image is inverted
and about half the
height of the object.
f
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”
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 !
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
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
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
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 2
f
C
Convex Spherical Image Formation
• The image forms at the intersection of any
two of the three rays behind the mirror.
Ray 1
Ray 2
The rays do not intersect in
front of the mirror!!
f
C
Sign conventions for mirrors (p. 538)
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.
Solving the problem
• Remember that for
convex mirrors, the
focal length and image
distance are always
negative.
1 1 1
 
p q f
1 1 1
1
1
  

 .049cm
q f p  35 49
q  20.42cm; The image is 20.42 cm behind the mirror
The Magnification of the Image
M 
q
 20.42

 .42
p
49
• Since the magnification is positive, the image is
upright and virtual
Ray diagram for the Image
f
C
Remember that you only need to draw two of the three rays to find the image.