Page 1
© 2017 Pearson Education, Inc. Slide 34-1
The figure shows a
concave mirror, a
mirror in which the
edges curve toward
the light source.
Rays parallel to the
optical axis reflect and
pass through the focal
point of the mirror.
Image Formation with Concave Spherical Mirrors
Page 2
© 2017 Pearson Education, Inc. Slide 34-2
A Real Image Formed by a Concave Mirror
Page 3
Sign conventions for spherical mirrors
• If the object point P is on the
same side as the incident
light, then s is positive.
• If the image point is on the
same side as the reflected
light, then is positive.
• If the center of curvature C is
on the same side as the
reflected light, then R is
positive.
Page 4
Spherical mirror with a point object
• A spherical mirror
with radius of
curvature R forms a
real image of the
point object P.
Page 5
Focal point and focal length
• When the object is very far
from the spherical mirror,
the incoming rays are
parallel.
• The beam of incident
parallel rays converges, after
reflection from the mirror, to
a focal point, point F.
• The distance from the vertex
to the focal point, denoted
by f, is called the focal
length.
Page 6
Focal point and focal length
• With the object at the focal
point, the reflected rays are
parallel to the optic axis.
• The reflected rays meet only
at a point infinitely far from
the mirror, so the image is
at infinity.
Page 7
© 2017 Pearson Education, Inc. Slide 34-7
For a spherical mirror with negligible thickness, the
object and image distances are related by:
where the focal
length f is related
to the mirror’s
radius of
curvature by:
The Mirror Equation
Page 8
Image of an extended object: Spherical mirror
• Shown is how to determine the position, orientation, and
height of an image formed by a concave spherical mirror.
Page 9
© 2017 Pearson Education, Inc. Slide 34-9
You see an upright, magnified image of your face
when you look into magnifying “cosmetic mirror.”
The image is located
QuickCheck 34.15
A. In front of the mirror’s surface.
B. On the mirror’s surface.
C. Behind the mirror’s surface.
D. Only in your mind because it’s a virtual image.
Page 10
Example 1 - A concave mirror forms an image, on a wall 3.00 m in front
of the mirror, of a headlamp filament 10.0 cm in front of the mirror. What
are the radius of curvature and focal length of the mirror? What is the
lateral magnification? What is the image height if the object height is
5.00 mm?
Page 11
Graphical method of locating images
Page 12
© 2017 Pearson Education, Inc. Slide 34-12
Example 2
A 3.0-cm-high object is located 20 cm from a concave
mirror. The mirror’s radius of curvature is 80 cm. Determine
the position, orientation, and height of the image.
Page 13
Example 3 - A concave mirror has a radius of curvature with absolute
value 20 cm. Show graphically the image of an object in the form of an
arrow perpendicular to the axis of the mirror at object distances of 30
cm, 20 cm, 10 cm, and 5 cm.
Page 14
Example 3 - A concave mirror has a radius of curvature with absolute
value 20 cm. Show graphically the image of an object in the form of an
arrow perpendicular to the axis of the mirror at object distances of 30
cm, 20 cm, 10 cm, and 5 cm.
Page 15
Example 4 – A object 0.600 cm tall is placed 16.5 cm to the left
of the vertex of a concave spherical mirror having a radius of
curvature of 22.0 cm. Draw a principal-ray diagram, showing the
formation of the image. Determine the position, size, orientation,
and nature of the image.
Page 16
In-class Activity #1 – A spherical, concave shaving mirror has
a radius of curvature of 32.0 cm. A 3.0 cm tall object with its
base on the optic axis is 12.0 cm to the left of the vertex of
the mirror? Determine the position, size, orientation, and
nature of the image.
Page 17
© 2017 Pearson Education, Inc. Slide 34-17
The figure shows parallel
light rays approaching a
mirror in which the edges
curve away from the light
source.
This is called a convex
mirror.
The reflected rays appear
to come from a point
behind the mirror.
Image Formation with Convex Spherical Mirrors
Page 18
© 2017 Pearson Education, Inc. Slide 34-18
A Real Image Formed by a Convex Mirror
Page 19
Image formation by a convex mirror
• If the mirror is convex, so that R is negative, the resulting
image is virtual (that is, the image point is on the opposite
side of the mirror from the object), erect, and smaller than the
object.
Page 20
Focal point and focal length of a convex mirror
• When incoming rays that are
parallel to the optic axis are
reflected from a convex
mirror, they diverge as
though they had come from
the virtual focal point F at a
distance f behind the mirror.
• The corresponding image
distance s is negative.
Page 21
Example 5 – A person looks at their reflection in a convex
mirror 0.750 m away. The radius of curvature is 7.20 cm.
The height of the person is 1.6 meters. Where and how tall
is the image of the person? Is it inverted?
Page 22
Graphical method of locating images
Page 23
Example 6 – A object 0.600 cm tall is placed 16.5 cm to the left
of the vertex of a convex spherical mirror having a radius of
curvature of 22.0 cm. Draw a principal-ray diagram, showing the
formation of the image. Determine the position, size, orientation,
and nature of the image.