Chapter 16
Light Waves and Color
Properties of Light Waves
(and all other waves)
 Polarization
 Reflection
 Refraction
 Interference
 Diffraction
Polarized Light
 How do polarizing sunglasses and camera
filters work?
 What is polarized light?
Recall that light is an electromagnetic wave consisting of
oscillating electric and magnetic fields:
 The oscillating electric field vector shown is in the
vertical plane, and the magnetic field is horizontal.
 Actually, the electric field could oscillate in the
horizontal with the magnetic field in the vertical plane,
or the electric field could oscillate at some angle to the
horizontal.
 As long as the electric field is always pointing in the
same direction for all the waves, the light is polarized.
 The electric field vector oscillates in a single
direction for polarized light.
 Unpolarized light has random directions of
orientation.
Light is usually
produced
unpolarized.
To make light
polarized,
something must
occur to select just
one direction of
field oscillation.
 Polarizing filters allows only that component
of each electric field vector that is aligned with
the filter’s axis of transmission to pass
through.
The component
perpendicular to
this axis is
absorbed.
 Reflection from a smooth surface of a
transparent material such as glass or water
can also polarize light.
Incoming sunlight is
unpolarized.
When the angle
between the reflected
wave and the
transmitted wave is a
right angle, the reflected
wave is polarized.
Polarizing sunglasses
can help reduce glare
from reflected sunlight.
 Many interesting and colorful effects are
related to the phenomenon of birefringence.



Birefringence is also called double refraction.
Light with different polarizations travels with
different velocities when passing through a
birefringent material.
This causes colorful displays when the birefringent
material is viewed through crossed polarizers.
Calcite crystals are
a good example of
birefringent material.
Lines are doubled
when viewed
through a calcite
crystal.
 Many interesting and colorful effects are
related to the phenomenon of birefringence.



Birefringence is also called double refraction.
Light with different polarizations travels with
different velocities when passing through a
birefringent material.
This causes colorful displays when the birefringent
material is viewed through crossed polarizers.
A plastic lens under
compression shows
stress birefringence
when viewed
between crossed
polarizers.
Reflection of light by a flat mirror

Consider plane wavefronts (no
curvature) approaching a flat
mirror at an angle:




After reflection they travel away
from the mirror with the same
speed as before reflection.
Some parts of the wavefront are
reflected sooner than others.
The reflected wavefronts have the
same speed and spacing but a
new direction.
The angle between the wavefronts
and the mirror is the same for the
emerging wave.
Law of Reflection


We usually measure the angles
with respect to the surface
normal, a line drawn
perpendicular to the surface of
the mirror.
The angle of incidence is equal
to the angle of reflection.
i   f

Refraction of Light
 What happens to light rays when they
encounter a transparent object such as glass
or water?
The speed of light in glass or
water is less than in air or
vacuum.
Thus, the distance between
wavefronts (the wavelength)
will be shorter.
The index of refraction is the
ratio of the speed of light c in a
vacuum to the speed of light v
in some substance.
c
n
v
 Since the wavefronts do not travel as far in one
cycle, the rays bend (much like rows in a marching
band bend when one side slows down by taking
smaller steps).



The amount of bending
depends on the angle of
incidence.
It also depends on the
indices of refraction of the
materials involved.
A larger difference in
speed will produce a
larger difference in indices
of refraction and a larger
bend in the wavefront and
ray.
Law of Refraction

When light passes from one
transparent medium to another,
the rays are bent toward the
surface normal if the speed of
light is smaller in the second
medium, and away from the
surface normal if the speed of
light is greater.

For small angles:
n11  n22
Interference of Light
Waves
 Is light a wave or a particle?
 If it is a wave, it should exhibit interference effects:
Recall that
two waves can
interfere
constructively
or
destructively
depending on
their phase.
Light from a single slit is split by passing through two slits,
resulting in two light waves in phase with each other.
The two waves will interfere constructively or destructively,
depending on a difference in the path length.
If the two waves travel equal distances to the screen, they
interfere constructively and a bright spot or line is seen.
If the distances traveled differ by half a wavelength, the two
waves interfere destructively and a dark spot or line appears
on the screen.
If the distances traveled differ by a full wavelength, the two
waves interfere constructively again resulting in another
bright spot or line.
The resulting interference pattern of alternating bright and
dark lines is a fringe pattern.
y
path difference  d
x

Red light with a wavelength of 630 nm strikes a double slit
with a spacing of 0.5 mm. If the interference pattern is
observed on a screen located 1 m from the double slit, how far
from the center of the screen is the second bright line from
the central (zenith) bright line?
= 630 nm = 6.3 x 10-7 m
d = 0.5 mm = 5 x 10-4 m
x=1m

path difference  2  d
y
x
7
2x 26.3 10 m1 m
y

 0.0025 m  2.5 mm
-4
d
5 10 m
 Similarly, interference can occur when light waves
are reflected from the top and bottom surfaces of a
soap film or oil slick.
 The difference in the path length of the two waves
can produce an interference pattern.
 This is called
thin-film
interference.
 Different wavelengths of light interfere constructively
or destructively as the thickness of the film varies.
 This results in the many different colors seen.
 The thin film may also be air between two glass
plates.
 Each band represents a different thickness of film.
Diffraction and Gratings
 The bright fringes in a double-slit interference
pattern are not all equally bright.


They become less bright farther from the center.
They seem to fade in and out.
 This effect, called diffraction, is due to
interference of light coming from different
parts of the same slit or opening.
When the path difference between light coming from the top
half of the slit and that coming from the bottom half is 1/2 of a
wavelength, a dark line appears on the single-slit diffraction
pattern.
x
The position of the first dark fringe is:
y
w

Light with a wavelength of 550 nm strikes a single slit that is
0.4 mm wide. The diffraction pattern produced is observed on
a wall a distance of 3.0 m from the slit. What is the distance
from the center of the pattern to the first dark fringe?
= 550 nm = 5.5 x 10-7 m
w = 0.4 mm = 4 x 10-4 m
x = 3.0 m
y
x
w
5.5 10 m3.0 m


 0.0041 m  4.1 mm
0.4 10 m
7
-3
How wide is the central bright fringe of this diffraction
pattern?
The central bright fringe extends out to the first dark fringe
on either side, so its width is just twice the distance y:
= 550 nm = 5.5 x 10-7 m
w = 0.4 mm = 4 x 10-4 m
x = 3.0 m
2y  24.1 mm   8.2 mm
 The diffraction pattern produced by a square opening
has an array of bright spots.
 Looking at a star or distant street light through a
window screen can produce a similar diffraction
pattern.
 A diffraction grating has a very large number of slits very
closely spaced.
 Whenever the path difference is equal to an integer multiple of
the light wavelength,
y
we get a strong bright fringe for
d  m, m  0,1,2,...
x
that wavelength.
 Different wavelengths will appear at different points on the
screen, spreading the light into its spectrum.

 Diffraction gratings in spectrometers are used to separate and
measure the wavelengths of light.
 Gratings also produce the effects seen in novelty glasses,
reflective gift wrappings, and in the colors seen on a CD.
Wavelength and Color
?
 How do we perceive
 What causes different objects
to have
?
 Why is the sky
?
Newton demonstrated that white light
is a mixture of colors.

He showed that white light from the sun, after being split into
different colors by one prism, can be recombined by a
second prism to form white light again.
How do our eyes distinguish color?



Light is focused by the cornea and lens onto the retina.
The retina is made up of light-sensitive cells called rods and
cones.
Three types of cones are sensitive to light in different parts
of the spectrum.
S cones are most sensitive to shorter wavelengths.
 M cones are most sensitive to medium
wavelengths.
 L cones are most sensitive to longer wavelengths.
 The sensitivity ranges overlap, so that light near the
middle of the visible spectrum will stimulate all three
cone types.

Light of 650 nm
wavelength stimulates L
cones strongest and S
cones weakest; the brain
identifies the color red.
Color Mixing
 The process of mixing two different
wavelengths of light, such as red and green, to
produce a response interpreted as another
color, such as yellow, is additive color mixing.
Combining the three primary colors
blue, green, and red in different
amounts can produce responses in
our brains corresponding to all the
colors we are used to identifying.
Red and green make yellow, blue
and green make cyan, and blue and
red make magenta.
Combining all three colors
produces white.
Color Mixing
 The pigments used in paints or dyes work by
selective color mixing.

They absorb some wavelengths of light more than
others.
When light strikes an
object, some of the light
undergoes specular
reflection: all the light is
reflected as if by a
mirror.
Color Mixing
 The selective absorption of light is a form of
subtractive color mixing.

In color printing, the three primary pigments are
cyan, yellow, and magenta.
Cyan absorbs red but transmits and
reflects blue and green.
Yellow absorbs blue but transmits and
reflects green and red.
Magenta absorbs at intermediate
wavelengths, but transmits and reflects
blue and red.
Why is the sky blue?
The white light coming from the sun is actually a mixture of light of
different wavelengths (colors).
The longer wavelengths of blue light are scattered by gas molecules
in the atmosphere more than shorter wavelengths such as red light.
The blue light enters our eyes after being scattered multiple times,
so appears to come from all parts of the sky.
Why is the sunset red?
The shorter wavelengths of blue light are scattered by gas molecules
in the atmosphere more than longer wavelengths such as red light.
When the sun is low on the horizon, the light must pass through more
atmosphere than when the sun is directly above.
By the time the sun’s light reaches our eyes, the shorter
wavelengths such as blue and yellow have been removed by scattering,
leaving only orange and red light coming straight from the sun.