Physics 1230: Light and Color
TOPIC 4 Geometrical optics - how do we
make images?
Ray tracing for mirrors (spotlights, Maglites,
auto mirrors, make-up and shaving mirrors,
globes, etc.)
http://www.colorado.edu/physics/phys1230
Mirrors
•  Lots of different kinds Shaving mirrors
Make-up mirrors
Rear and side view mirrors
Globes
•  Unlike flat mirrors, some of the above mirrors
make the image bigger while others make the
image smaller
•  In some cases what you see depends on how close
you are to the mirror
Materials like metals with many mobile electrons can cancel
out the light wave field in the forward direction so there is no
transmission but only reflection for certain wavelengths.
•  Metals reflect all waves below
a certain frequency
–  the plasma frequency - which
varies from metal to metal
•  Silver is particularly
interesting because it reflects
light waves at all visible
frequencies
–  Its plasma frequency is at the
top of the violet so it reflects
all of the wavelengths below
and appears whitish
•  Gold and copper have a
yellowish-brownish color
because they reflect greens,
yellows and reds but not blues
or violets
–  Red and green make yellow
What is a mirror?
•  Since silver is such a good
reflector, a coating of
silver on glass makes a good
(common) mirror.
•  If the silver coating is thin
enough the mirror can be
made to transmit 50% of
the light and to reflect the
other 50%
–  This is called a halfsilvered mirror
–  A half-silvered mirror
used with proper
lighting can show
objects on one side or
the other of the mirror
One-way Mirror: needs the correct lighting!
FLAT or PLANE Mirrors - Surface of mirror is flat
We interpret all rays coming into our
eye as traveling from a fictitious
image in a straight line to our eye
even if they are reflected rays!
http://micro.magnet.fsu.edu/primer/lightandcolor/mirrorsintro.html
History of Mirrors
Predating even crude lenses, mirrors are perhaps the oldest optical element
utilized by man to harness the power of light. Prehistoric cave dwellers were
no doubt mesmerized by their reflections in undisturbed ponds and other
bodies of water, but the earliest man-made mirrors were not discovered until
Egyptian pyramidal artifacts dating back to around 1900 BC were examined.
Mirrors made during the Greco-Roman period and the Middle Ages consisted
of highly polished metals, such as bronze, tin, or silver, fashioned into
slightly convex disks, which served mankind for over a millennium.
http://micro.magnet.fsu.edu/primer/lightandcolor/mirrorsintro.html
Archimedes’ Death Ray
(Syracuse ca. 213 BC)
At last in an incredible manner he
[Archimedes] burned up the whole
Roman fleet. For by tilting a kind of
mirror toward the sun he
concentrated the sun's beam upon
it; and owing to the thickness and
smoothness of the mirror he ignited
the air from this beam and kindled a
great flame, the whole of which he
directed upon the ships that lay at
anchor in the path of the fire, until
he consumed them all.
History of Mirrors
It was not until the late Twelfth or early
Thirteenth Centuries that the use of glass
with a metallic backing was developed to
produce looking glasses, but refinement of
this technique took an additional several
hundred years. By the sixteenth century,
Venetian craftsmen were fabricating
handsome mirrors fashioned from a sheet of
flat glass coated with a thin layer of
mercury-tin amalgam. Over the next few
hundred years, German and French
specialists developed mirror-making into a
fine art, and exquisitely crafted mirrors
decorated the halls, dining, living, and
bedrooms of the European aristocracy.
CURVED MIRROR REFLECTION AND IMAGES
•  Is there a difference between the reflection of yourself in a shaving/
make-up mirror, or a corner viewing mirror, or your reflection in a
round ornament?
•  What kind of mirror directs your car headlights, or a maglite beam,
forward?
•  What kind of mirrors are used in very large telescopes?
CONCEPT QUESTION
In your make-up/shaving mirror, your image is A)  Smaller
B)  Bigger
C)  Same size
D)  Upside down
CONCEPT QUESTION
In a globe ornament, your
image is A)  Smaller
B)  Bigger
C)  Same size
CONCEPT QUESTION
Compared to your own size, your reflection from a pond is A)  Smaller
B)  Bigger
C)  Same size
D)  More flattering
mirror movie
http://www.rofl.to/
awesome-mirror-prank
mountain reflection
LAW OF REFLECTION
Angle of Incidence = Angle of Reflection
normal to surface
ϑi ϑr
glass or metal
LAW OF REFLECTION
Angle of Incidence = Angle of Reflection
normal to surface
ϑi ϑr
glass or metal
Making Images - definitions
•  OBJECT: This is the thing you see an image of.
•  VIRTUAL IMAGE: This is an image formed in a different place
other than where the light is coming from. If you reach out to try to
touch the image, your hand would hit the lens or mirror and not be
able to touch the image. It is your psychological impression of where
something is.
•  REAL IMAGE: This is an image formed in the air between you and
the mirror or lens. You can stick your hand through this ghost-like
image or see it on a screen.
•  Demonstrations
How is an image produced in a mirror?
The meaning of a virtual image
•  If we trace rays for every ray from
every part of Alex which reflects in the
mirror
– 
we get a virtual image of the real Alex
behind the mirror. It is virtual because
there is no light energy there, no real
rays reach it, and it cannot be seen by
putting a screen at its position!!
Bob looks at
Alex's image
Alex
•  When all of the reflected rays from
Alex's chin are traced backwards they
all appear to come from the virtual
image of his chin
– 
Hence Alex's image is always in the
same place regardless of where Bob
looks
•  The image chin is behind the mirror
by a distance = to the distance the
real chin is in front of the mirror
– 
– 
– 
This is true for all parts of Alex's
image
Alex's virtual image is the same size
as the real Alex
Alex's image is further away from Bob
than the real Alex
Mirror
Bob sees Alex's image
in the same place
wherever he moves his
head
Virtual image of Alex
is behind the mirror
For simple (flat) mirrors the image location is
therefore predictable without knowing where the
observer's eye is and without ray-tracing
Mirror
Mirror
Mirror
Mirror
Spherical Mirrors
•  Spherical mirrors appear to be cut from a section of a sphere.
They can be concave or convex
•  Each obeys the law of reflection
•  BUT each kind of mirror makes a different kind of image
concave
convex
Definitions for Spherical Mirrors
•  Radius of Curvature: The radius of the sphere the mirror is “cut from”
•  Center of Curvature: The center of the sphere the mirror is cut from
•  Focal Point: The point where rays from a distance appear to converge
•  Focal Distance: The distance of the focal point from the mirror
•  Paraxial Ray: A ray coming on to the mirror parallel to the axis
concave
convex
paraxial ray
F C
axis
paraxial ray
C F
axis
radius of
curvature
focal point (F)
center of curvature (C)
focal point (F)
How do rays behave at spherical mirrors?
•  We already know that “angle of incidence = angle of reflection”
•  However, this would take a lot of time if we tried to apply it to every ray
•  Instead we use the following “rules” for curved mirrors
•  RULE #1: All rays parallel to the axis are reflected such that they appear
to come from the focal point F
(notice that a ray coming in along a radius will have zero angle with respect to
the normal, and so will be reflected back on itself)
How do rays behave at spherical mirrors?
•  RULE #1: All rays parallel to the axis are reflected such that they appear to
come from the focal point F
F
.
C
concave
C
F
convex
How do rays behave at spherical mirrors?
•  RULE #2: Incident rays coming towards the center of curvature are reflected
back on themselves. Why?
concave
mirror
.
C
concave
C
convex
How do rays behave at spherical mirrors?
•  RULE #3: Incident rays headed for F are reflected so that they are parallel to
the axis.
(notice that this rule is just the reverse of Rule #1)
C
F
concave
C
F
convex
How do we make images using spherical mirrors?
•  RULE #1: All rays parallel to the axis are reflected such that they appear to
come from the focal point F
•  RULE #2: Incident rays coming towards the center of curvature are reflected
back on themselves
•  RULE #3: Incident rays headed for F are reflected so that they are parallel
to the axis.
Images in convex mirrors
Another rule: parallel light rays
•  All parallel light rays coming in to a concave focusing mirror will be brought to a
focus in a plane that includes the focal point.
• Note that this rule applies to rays that are parallel to themselves – they do not
have to be parallel to the axis.
How do we make images using spherical mirrors?
•  RULE #1: All rays parallel to the axis are reflected such that they appear to
come from the focal point F
•  RULE #2: Incident rays coming towards the center of curvature are reflected
back on themselves
•  RULE #3: Incident rays headed for F are reflected so that they are parallel
to the axis.
Images in convex mirrors
Where is the focal point F for a curved mirror?
•  The focal point F is at half the distance from the mirror to the radius of
curvature C on the main axis
•  This can be seen to be approximately correct from the law of reflection. It is
also proved in Appendix C of the textbook.
How do we make images using spherical mirrors?
•  RULE #1: All rays parallel to the axis are reflected such that they appear to
come from the focal point F
•  RULE #2: Incident rays coming towards the center of curvature are reflected
back on themselves
•  RULE #3: Incident rays headed for F are reflected so that they are parallel
to the axis.
Images in concave mirrors
Concept question: How would you draw in other
rays e.g. purple rays?
A.  By drawing them close to the existing rays
B.  Using the law of reflection
C.  Using a different rule
Images in concave mirrors
How do we make images using spherical mirrors?
•  RULE #1: All rays parallel to the axis are reflected such that they appear to
come from the focal point F
•  RULE #2: Incident rays coming towards the center of curvature are reflected
back on themselves
•  RULE #3: Incident rays headed for F are reflected so that they are parallel
to the axis.
Images in concave mirrors
Spherical Mirror Simulations
Applet on Convex Mirrors
http://micro.magnet.fsu.edu/primer/java/
mirrors/convexmirrors/index.html
Applet on Concave Mirrors
http://micro.magnet.fsu.edu/primer/java/
mirrors/concavemirrors/index.html
Concept Question
Is your make-up/shaving mirror A)  Flat
B)  Concave
C)  Convex
Collecting radiation using parabolic reflectors
radio telescope
radar transmitter
parabolic
microphone
headlamp
parabolic trough
Parabolic mirrors as
solar concentrators
parabolic dish
array
superheated
steam
generation
How does your car switch between high and low
beams?
radar transmitter