Chapter 34A - Reflection
and Mirrors (Geometrical)
A PowerPoint Presentation by
Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
©
2007
Objectives: After completing this
module, you should be able to:
• Explain and discuss with diagrams, reflection,
absorption, and refraction of light rays.
• Illustrate graphically the reflection of light
from plane, convex, and concave mirrors.
• Define and illustrate your understanding of
real, virtual, erect, inverted, enlarged, and
diminished as applied to images.
• Use geometrical optics to draw images of an
object at various distances from converging
and diverging mirrors.
Geometrical Optics
In the study of how light behaves, it is
useful to use “light rays” and the fact
that light travels in straight lines.
When light strikes the
boundary between
two media, three
things may happen:
reflection, refraction,
or absorption.
Air
absorption
reflection
Water
refraction
Reflection, Refraction, and
Absorption
Air
Reflection: A ray
from air strikes
the water and
returns to the air.
Refraction: A ray
bends into the
water toward the
normal line.
absorption
reflection
Water
refraction
Absorption: A ray is
absorbed atomically
by the water and
does not reappear.
The Laws of Reflection
1. The angle of incidence qi is equal
to the angle of
reflection qr :
Air
N
reflection
qi qr
Water
qi = qr
All ray angles are measured with respect to normal N.
2. The incident ray, the
reflected ray, and
the normal N all lie
in the same plane.
3. The rays are
completely
reversible.
The Plane Mirror
A mirror is a highly polished surface that
forms images by uniformly reflected light.
Note: images
appear to be
equi-distant
behind mirror
and are rightleft reversed.
Definitions
Object distance: The straight-line distance p
from the surface of a mirror to the object.
Image distance: The straight-line distance q
from the surface of a mirror to the image.
Object
distance
=
Image
distance
Object
Image
p=q
qi = qr
p
q
Real and Virtual
Real images and
objects are formed
by actual rays of
light. (Real images
can be projected on
a screen.)
Virtual images and
objects do not really
exist, but only seem
to be at a location.
Light rays
Real
object
No light
Virtual
image
Virtual images are on the
opposite side of the mirror
from the incoming rays.
Image of a Point Object
Plane mirror
q=p
Real
object
p
q
Virtual
image
Image appears to be at same distance
behind mirror regardless of viewing angle.
Image of an Extended Object
Plane mirror
q=p
p
q
Virtual
image
Image of bottom and top of guitar
shows forward-back, right-left reversals.
Terms for Spherical Mirrors
A spherical mirror is
formed by the inside
(concave) or outside
(convex) surfaces of
a sphere.
A concave spherical
mirror is shown here
with parts identified.
The axis and linear
aperture are shown.
Concave Mirror
R
V
Axis
C
Linear
aperture
Center of Curvature C
Radius of curvature R
Vertex V
The Focal Length f of a Mirror
Incident parallel ray
C
R
F
qi
qr
axis
Focal point
The focal length, f
V
f
Since qi = qr, we
find that F is midway between V
and C; we find:
The focal
length f is:
R
f 
2
The focal length f is equal to half the radius R
The Focus of a Concave Mirror
The focal point F for a concave mirror is the point
at which all parallel light rays converge.
F
For objects located at infinity,
the real image
appears at the
focal point since
rays of light are
almost parallel.
Focal point
R
f 
2
Incident parallel Rays
axis
C
The Focus of a Convex Mirror
The focal point for a convex mirror is the point F
from which all parallel light rays diverge.
Virtual focus;
reflected rays
diverge.
Incident Rays
R
C
R
f 
2
F
axis
Reflected Rays
Image Construction:
Ray 1: A ray parallel to mirror axis passes
through the focal point of a concave mirror
or appears to come from the focal point of a
convex mirror.
Ray 1
C
F
Object
Concave mirror
Convex
mirror
C
F
Ray 1
Object
Image Construction (Cont.):
Ray 2: A ray passing through the focus of a
concave mirror or proceeding toward the
focus of a convex mirror is reflected parallel
to the mirror axis.
Ray 1
C
Ray 2
Convex
mirror
Ray 1
F
Image
Concave mirror
Ray 2
C
F
Image
Image Construction (Cont.):
Ray 3: A ray that proceeds along a radius is
always reflected back along its original path.
Ray 1
Ray 3
Ray 1
Ray 2
Ray 2
C
Concave
mirror
F
C
Ray 3
Convex
mirror
F
Image
The Nature of Images
An object is placed in front of a concave mirror.
It is useful to trace the images as the object
moves ever closer to the vertex of the mirror.
We will want to locate the image and answer
three questions for the possible positions:
1. Is the image erect or inverted?
2. Is the image real or virtual?
3. Is it enlarged, diminished, or the same size?
Object Outside Center C
1. The image is inverted;
i.e., opposite of the
object orientation.
2. The image is real; i.e.,
formed by actual light
rays in front of mirror.
3. The image is diminished
in size; i.e., smaller
than the object.
Ray 1
Ray 2
C
Concave
mirror
F
Ray 3
Image is located
between C and F
Object at the Center C
1. The image is inverted;
i.e., opposite of the
object orientation.
2. The image is real; i.e.,
formed by actual light
rays in front of mirror.
3. The image is the same
size as the object.
Ray 1
Ray 2
C
F
Ray 3
Image is located
at C, inverted.
Object Between C and F
1. The image is inverted;
i.e., opposite of the
object orientation.
2. The image is real; i.e.,
formed by actual light
rays in front of mirror.
3. The image is enlarged
in size; i.e., larger than
the object.
Ray 1
Ray 3
C
F
Ray 2
Image is outside
of the center C
Object at Focal Point
When the object is
located at the focal
point of the mirror,
the image is not
formed (or it is
located at infinity).
The parallel reflected
rays never cross.
Ray 3
Ray 1
C
F
Reflected rays
are parallel
Image is located at
infinity (not formed).
Object Inside Focal Point
1. The image is erect;
i.e., same orientation
as the object.
2. The image is virtual;
that is, it seems to be
located behind mirror.
3. The image is enlarged;
bigger than the object.
C
F
Erect and
enlarged
Virtual
image
Image is located
behind the mirror
Observe the Images as
Object Moves Closer to Mirror
C
Ray Ray
1 1
Ray
11
Ray
2
Ray
2
Ray
Ray 3
C
C C C FF
F
F
Virtual
Rayrays
3image
Erect
and
Reflected
Concave
Ray
Ray
3 2
enlarged
are
parallel
mirror
Convex Mirror Imaging
Convex
mirror
Ray 1
Convex
mirror
Ray 1
2
Ray 2
C
F
Image
C
F
Image gets larger
as object gets
closer
All images are erect, virtual, and diminished.
Images get larger as object approaches.
Converging and Diverging Mirrors
Concave mirrors and
converging parallel rays will
be called converging mirrors
from this point onward.
Converging Mirror
C
Convex mirrors and
diverging parallel rays will
be called diverging mirrors
from this point onward.
Diverging
Mirror
F
C
Concave
F
Convex
Summary
Reflection: A ray
from air strikes
the water and
returns to the air.
Air
absorption
reflection
Water
refraction
Refraction: A ray
bends into the
water toward the
normal line.
Absorption: A ray is
absorbed atomically
by the water and
does not reappear.
Summary (Cont.)
1. The angle of incidence qi is equal
to the angle of
reflection qr :
Air
N
reflection
qi qr
Water
qi = qr
All ray angles are measured with respect to normal N.
2. The incident ray, the
reflected ray, and
the normal N all lie
in the same plane.
3. The rays are
completely
reversible.
Summary (Definitions)
Object distance: The straight-line distance p
from the surface of a mirror to the object.
Image distance: The straight-line distance q
from the surface of a mirror to the image.
Real image: An image formed by real light
rays that can be projected on a screen.
Virtual image: An image that appears to be at
a location where no light rays reach.
Converging and diverging mirrors: Refer to the
reflection of parallel rays from surface of mirror.
Image Construction Summary:
Ray 1: A ray parallel to mirror axis passes
through the focal point of a concave mirror
or appears to come from the focal point of a
convex mirror.
Ray 2: A ray passing through the focus of a
concave mirror or proceeding toward the
focus of a convex mirror is reflected parallel
to mirror axis.
Ray 3: A ray that proceeds along a radius is
always reflected back along its original path.
Summary (Cont.)
For plane mirrors, the object distance equals
the image distance and all images are erect and
virtual.
For converging mirrors and diverging mirrors,
the focal length is equal to one-half the radius.
All images formed from convex mirrors are
erect, virtual, and diminished in size.
Except for objects located inside the focus
(which are erect and virtual), all images formed
by converging mirrors are real and inverted.
CONCLUSION: Chapter 34A
Reflection and Mirrors
(Geometrical)