Properties of Light   
Chapter 12

 Joseph F. Alward, PhD
 Department of Physics
 University of the Pacific


  Law of Reflection                                                      
Angle of Reflection
= Angle of Incidence

 Angles are measured with
 respect to the normal line
 (the perpendicular line).



 Reflection Law Example    
Example Problem:

  90 - 65 = 25
180 - 120 - 25 = 35
  90 - 35 = 55


  Billiards and Mirrors

A ball bouncing off the
bank of a pool table
behaves like a light
ray reflecting off a
mirror.  To bank the
cue ball into another
ball (the object ball),
imagine you are
shooting at the mirror
image of the object

Billiards and Mirrors
This applet allows
placement and speed
of cue ball.




  Specular vs Diffuse Reflection                               



   Diffuse Reflection

 Rough surfaces consist of a large number
 of different specularly-reflecting planes.

 Visible light reflects diffusely from

   Specular and Diffuse Reflection
Rough surfaces seem smooth
for very long-wavelength
electromagnetic waves.

This parabolic dish reflects
long wavelength radio waves
to the detector, but reflects
most of the shorter wavelength
radiation away from the



 Specular vs Diffuse Reflection                                                                   
The cruiser Aurora, which
played an important role in
the communist revolution
in 1917, is docked on the
River Neva at St. Petersburg,

When the water is still,
reflection is specular.  The
image blurs when the
water is rough.

(Eugene Hecht, Physics)




   Specular versus Diffuse Reflection
What kind of reflections
account for the column
of light reflected off
the water?

What would we see on
the water if it were
perfectly flat, unmoving?




  Plane Mirror Geometry        

 Light from the castle appears to be
 coming from a point behind the mirror


 Virtual Images in Plane Mirrors                                    
  If light energy doesn't flow from the image,
  the image is "virtual".
Rays seem to come from behind
the mirror, but, of course, they
don't.  It is virtually as if the rays
were coming from behind the

"Virtually":  the same as if

As far as the eye-brain system is
concerned, the effect is the same
as would occur if the mirror were
absent and the chess piece
(castle) were actually located at
the spot labeled "virtual image".




   Image vs Object Distance
Flat mirror images are as far
behind the mirror as is the

About 4 percent of light is
reflected off a windowpane.



   The Law of Reflection                                                                                    
  The girl in Edouard Manet's
painting,  The Bar at the
, is
standing in front of a large
plane mirror.

We see reflected in it her back
and the face of a man she
seems to be talking to.

From the law of reflection what
if anything, is wrong with this

(Eugene Hecht, Physics)

   The Law of Reflection                                                                                      
  The Toilet of Venus, by
Diego Velasquez.

What does Venus see
in the mirror?

(Eugene Hecht, Physics)


    Left-Right Reversal  
The woman's image is as
far behind the flat mirror
as she is in front of it.

Note the that "woman" in
the mirror is coming her
hair with her left hand.



  Left-Right Reversal                                                                                  


The printing is reversed when viewed in a rear-
view automobile mirror.


   Convex and Concave Mirrors

 Images in convex mirrors                                              Images in concave mirrors
 are always smaller.                                                          are always bigger.





   Convex Mirrors

Images in convex mirrors are always smaller
than the object.

           (M.C. Eshcher) 




   Convex Mirrors

 The Hubble Mirror                               
  Images are always
smaller in a convex

What type of mirror
is the Hubble mirror?

What is the person
in the mirror pointing

Concave Make-Up Mirror                                                                                             



  Concave Mirror Focuses Colors         

 White light is formed where red, blue, and green overlap.



  Concave Mirror Focal Point             

 Rays' paths are determined by the angle law.


  1.  Concave Mirror Animation  
  2.  Diverging Mirror  



   Refraction:  The Bending of Wavefronts                     

One side of wave front slows down,
and the entire train of fronts twists.




  Understanding Refraction

   Refraction Terminology
Angles are measured with
respect to the line which is
perpendicular to the

When light travels from one
medium--such as air, to
another one of higher
density--such as water,
usually the light ray bends
toward the perpendicular


  Apparent Depth in Water                                                       

 Light exits into
 medium (air)
 of lower index
 of refraction,
 and turns left.


  More Apparent Depth                                                                                
Spear-fishing is made more
difficult by the bending of

To spear the fish in the figure,
one must aim at a spot in
of the apparent location
of the fish.



A FishEye's View of the World
(Excellent applet illustrating refraction)


  Refraction at Sunset      
The sun actually falls below below the
horizon, i.e., it "sets", a few seconds
before we see it set.




  Flattening of the Sun at Sunset                                     

  Bottom of sun appears flattened at sunset.

 Rays from top of sun are also
 refracted, but not as much because
 they enter the atmosphere at a less
 oblique angle.  Thus, the top of the
 sun is also flattened, but not as
 much as the bottom.



 Water on Road Mirage                                

    There's no water on the road; why does it appear so?



  Water on Road Mirage


  Explaining the Water Mirage                                                  

  Differential Color Refraction                              

Note that the shorter wavelengths of light are bent more than the longer; blue more than red.





 Dispersion through Prism





 Refraction in a Raindrop                                                        

  Violet is bent more than red.



  Forming a Rainbow                                    
An observer sees
red light coming
from droplets of
water higher in
the sky, while
droplets of water
lower in the sky
send violet light
to the eye.


   The Shape of the Rainbow
All of the droplets of water
along the arc shown in the
figure are equivalent.  

A rainbow would form a
complete circle, not just
an arc, if the ground
didn't get in the way.


  Understanding Rainbow Geometry


Rainbows always face the
observer.  As the observer
moves, the rainbow moves.

One can never get to the
"pot of gold" at the end of
the rainbow.


    Double Rainbows
The secondary rainbow
displays colors in the
reverse order.

Looking below about
42 degrees, the sky
is relatively bright, and
acts like a mirror to the

Above 42 degrees, the
water absorbs most of
the sunlight, and the
sky is darker.

   Double Rainbows Explained

  One reflection in a primary rainbow

  Two reflections in a secondary rainbow droplet.

   Internal Reflection                                              
 All rays reflect internally, but
 the top three rays reflect only
 a small percentage internally;
 most energy leaves the prism.
 The fourth and fifth rays are
 reflected 100 % internally.



   Internal Reflection and the Critical Angle
Critical angle is 48 degrees. Any ray which strikes the
surface from inside
the water at an angle
greater than 48 degrees will not escape the water.




Internal Reflection Applet



   The View from Below the Water
Rays A, B, and C
from the bottom
of the pond are
totally internally

Outside the 96-
degree cone, the
fish sees only
light reflected
from the bottom
of the pond.






A FishEye's View of the World
(Excellent applet illustrating refraction)





  Internal Reflections in Prisms

   Prisms in Binoculars
Magnifying power
of binoculars is
made larger by
increasing the
path length
traveled between
the two lenses.




  Total Internal Reflection in Diamond
The critical angle for
diamond in air is
24.5 degrees

  Internal Reflections in Diamond
The critical angle for diamond
in air is 24.5 degrees; any ray
which strikes the surface on the
inside at an angle of greater
than 24.5 degrees will not
escape the diamond.

   Optical Fibers




 Optical Fiber                                             



  Optical Fibers in Medicine                                                                                  

 Arthroscopic Surgery                              Bronchoscope                                            Colonoscope


     Convex Lenses                                                               






   Convex Lenses



  The Convex Lens    
  as a Magnifier




 Convex Lenses Used as Magnifiers




    Concave Lenses

   The De-Magnifier




  Convex Lens is Inverse  
  of Concave Lens





Surface of water is like a collection of lenses which change shape.  Changing air
densities explain why stars twinkle.



  Image Formation 

Without angle-selectivity, light from all parts of the object overlap all parts of the wall.
Pinhole in box, or a lense directs rays from one part of the object to only one point
on the screen.  

In bright light , the eyes' pupils becomes smaller, allowing sharper images to form.





   Image Formation with Lenses
If object is
far from the
lens (beyond)
the focal
point, a real
inverted image
is formed.





   Film Projectors                                                              


  Camera Film Image          





 1.  Converging Lens Interactive Applet  
 2.  Diverging Lens Interactive Applet



  Spherical Aberration             

   Rays away from the center are not focused at
   the focal point.




 Chromatic Aberration   

 Different colors refract by different






  Important Persons in Early 20th Century Physics

                                  Solvay Conference, 1911
Einstein explained the
photoelectric effect by
assuming that
electromagnetic energy
(light) manifests itself as
quanta of energy--or,
"photons"--of energy hf:

 E = hf  

f = frequency of light



 Duality of Light
Light acts like a wave when
it's moving from one place
to another, but when it
interacts with matter, it acts
like a particle.




   Photocells in Garage Door Openers
Light to photocell
is interrupted, and
the corresponding
drop in photocurrent
signals the motor to




  Photocells in Movie Film
Optical sound track is like
a bar-code, but much more
detailed.  Track modulates
the intensity of the light
at a frequency which is the
same as the sound which
was used to produced the