Electromagnetic Waves
The Electromagnetic Spectrum
 Our eyes are only able to see visible light.
 Night-vision goggles expand a person’s
“sight” to include infrared waves.
The Electromagnetic Spectrum
Color and Frequency
 Different frequencies of light correspond to
different colors.
 ROYGBIV is the list of colors in order of
increasing frequency (decreasing
wavelength)
Speed of Electromagnetic Waves
 All electromagnetic waves travel at the same
speed:
THE SPEED OF LIGHT (c)
In a vacuum:
2.97792 x 108 m/s
In air:
2.97709 x 108 m/s
So for the most part, c = 3.00 x 108 m/s
Wave Equation
 Remember v = f ∙ λ
 So…… for Electromagnetic Waves,
c=f∙λ
speed of light = frequency ∙ wavelength
Light – Wave or Particle?
 Throughout history, light has been
described as both a particle and a
wave.
 Current model incorporates
aspects of BOTH particle and
wave theories.
 For now, let’s focus on the wave
model since it best suited for an
introductory discussion of light.
OPTICS
 LASER
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LIGHT
AMPLIFICATION of
SIMULATED
EMMISION OF
RADIATION
Laser light vs. White light
 White light (like from the sun or from an
incandescent light bulb) is composed of many
different frequencies.
 Even light of a single frequency (color) has
some light waves in phase and some out of
phase.
 LASER light has light of a single frequency
and the waves are in phase with each other.
Seeing Laser Light
 We cannot see laser beam through clean air
or water.
 If we add something to the air or water to
make it cloudy, we can see the beam
because of scattering
Reflection
 Remember that when a wave meets a hard
boundary, it is REFLECTED.
 On a smooth surface, like a mirror, we call it
specular reflection.
 On a rough surface, like a piece of paper or
table top, we call it diffuse reflection.
Law of Reflection
Angle of incidence θi = Angle of reflection θr
Law of Reflection
 Still holds for diffuse reflection at each spot!
Application to Pool!
Ray Diagrams
 We can use ray diagrams to locate an image
formed by a mirror with simple geometry.
 An image formed
by rays that appear
to come from
behind the mirror
is called a
virtual image.
Curved (Spherical) Mirrors
Convex Mirrors
 Convex mirrors produce small, upright
images when far away from object.
 Up close, the image gets more life-size and
its still upright.
Concave Mirrors
 Concave mirrors produce small, inverted
images when the object is far away.
 Up close, the image gets larger and becomes
upright and REALLY LARGE
Focal Point
 Horizontal rays hitting a convex mirror reflect
off as if they were coming from a point behind
the mirror. This is called the focal point.
f = R/2
Focal Point
 For a concave mirror, the focal point is where
the horizontal rays would meet after reflecting
Terms
 Focal Length = f
 Image distance = di
 Image height = hi
Object distance = do
Object height = ho
Flipping of image on concave mirror
Real image: an image formed by light rays that
can be seen on a screen
Virtual image: an image from which light rays
appear to diverge, even though they are not
actually focused there.
“L.O.S.T.” Summary
for blue image of red arrow object
Location
Front or Behind
Mirror? How far?
- Orientation?
Right-side-up or
Up-side-down?
- Size?
-
Larger or Smaller
than object?
Type?
Real or
Virtual?
Mathematical Relationships
 Focal length, object and image distances
have a positive sign when on the mirror’s
front side
 Focal length and image distances on the
back side of a mirror have a negative sign.
Magnification
 For an image in front of a mirror, M is
negative and the image is inverted.
 For an image behind the mirror, M is positive
and the image is upright.
Spherical Aberration
 Aberration: defined by Webster’s dictionary as “a
departure from the expected or proper course”.
 Spherical mirrors have an aberration. Not all
rays focus in the same location.
 This is most notable for rays striking the outer
edges of the mirror (away from principle axis).
 Result is that image from spherical mirror
usually blurry.
Parabolic Radio Telescopes
White Light
 White light (comprised of all the colors
together) can be separated by a prism.
 This is called dispersion
Additive Primary Colors of Light
 Adding red, blue
and green light
results in white
light
 When added in
varying proportions,
they can form all
of the colors of the
spectrum
Secondary Colors of Light
Red + Green = Yellow
R+G=Y
Red + Blue = Magenta
R+B=M
Blue + Green = Cyan
B+G=C
Since adding Red and Cyan is the
same as adding Red + Blue + Green,
Red and Cyan are said to be
COMPLEMENTARY COLORS of
each other
Complementary Colors of Light
 Red and Cyan
 Blue and Yellow
 Green and Magenta
-because added together,
they would make white light!
R + C = R + (B + G) = W
B + Y = B + (R + G) = W
G + M = G + (B + R) = W
 Principles of color addition
have important applications
to color television, color
computer monitors and onstage lighting at the
theaters. Each of these
applications involves the
mixing or addition of colors
of light to produce a desired
appearance.
Why is the Sky Blue?
Violet and Blue light is
scattered the most by
the atmosphere.
Our eyes are not very
sensitive to Violet light so
we see the sky as Blue.
Color of objects
 Objects absorb some wavelengths of light
and reflect other wavelengths of light.
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Under different lighting conditions, the color
of objects may appear different.
Common Misconception
 The color of an object does not reside in the
object itself. Rather, the color is in the light
that shines upon the object and that
ultimately becomes reflected or transmitted to
our eyes.
Pigments
 Pure pigments absorb a single frequency or
color of light.
 The color of light absorbed by a pigment is
merely the complimentary color of that
pigment!
Blue pigment absorbs Yellow light
Yellow pigment absorbs Blue light
Green pigment absorbs Magenta light
Magenta pigment absorbs Green light
Red
“
Cyan
Cyan
“
Red
Why Does the Ocean Appear
Blue?
Red light is absorbed, so the
reflected light from the water
is Cyan
Questions:
1. Magenta light shines on a piece of paper
with yellow pigment. What color does the
paper look?
M – B = (R + B) – B = R
Red!
Questions:
 2. Yellow light shines on a piece of paper
with red pigment. What color does the paper
look?
Y- C
(R + G) – (B + G)
R + G – G (no blue light to
reflect)
= R Red!
=
=
Questions:
 3. Yellow light shines on a piece of paper
with blue pigment. What color does it look?
Questions:
 3. Yellow light shines on a piece of paper
with blue pigment. What color does it look?
Y – Y = ?????
The absence of light is what we see as BLACK
Polarization
 How do polarized sunglasses reduce glare?
Polarization
 Most light is made up of transverse
electromagnetic waves that are oscillating in
random directions (unpolarized)
 Some materials can filter out all waves of light
except for those lined up in a particular
direction.
 This light would be said to be polarized.
Polarized Sunglasses
 Light that reflects off at glancing angles of the
road, or water, or glass tends to be
horizontally polarized.
 Polarized Sunglasses have an axis that is
vertical so glare from horizontal surfaces is
eliminated.
The Blue Sky is Polarized!
 In general, the sky is partially polarized
tangential to a circle centered in the sun and
maximum polarization is found at ninety
degrees from it. Therefore, at noon when the
sun is directly overhead, the sky will be
polarized horizontally along the entire
horizon.
 http://www.atoptics.co.uk/fz1013.htm
A polarizing filter on a camera
makes the sky look more blue…
Refraction
 As light travels from one medium to another,
it changes speed. This change in speed
results in a bending of the light ray. We say it
is REFRACTED.
Reflection AND Refraction
 Sometimes, light is partially reflected and
partially refracted. The Law of Reflection still
holds.
Index of Refraction
 The ratio of the speed of light in a vacuum
(c= 3.00 x 108 m/s) to the speed of light in a
given material (v) is called the index of
refraction (n)
n = speed of light in a vacuum = c
speed of light in a material v
nair = 1.0003
ndiamond = 2.417
(slowed down by <½)
Snell’s Law
n1sinθ1 = n2 sinθ2
Notice that when light is slowed down as it
enters a material, it is refracted towards the
normal. When it speeds up, it is refracted
away from the normal.
Calculator Help
 Make sure calculator set to degrees (not radians !)
 Know how to use sin and sin-1 functions.
 Example
1.0003 sin 32°= 1.54 sin θ2
-multiply 1.0003 times the sin 32 = .5300
-then divide by 1.54 to get .3442
-then take the sin-1 of .3442 to get 20.1°
Total Internal Reflection
 Light going from water to air
 Increase θ1 gradually
 Eventually reach a θCRITICAL where light is
totally internally reflected
 As long as θ1 is > θCRITICAL you get TIF
Total Internal Reflection
 Applications:
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Reflectors
Driveway markers
Binoculars
Fiber optics
Fountains
Total Internal Reflection
 For any interface between two materials,
there is a unique critical angle.
 Some materials have a critical angle that is
not very large, so light becomes “trapped”
inside the material.
 Diamond has a critical angle of about 25°.
 Light entering a diamond strikes many of its
internal surfaces before striking one at less
than 25° and emerging.
TIF in Diamonds
How to Find Critical Angle
 To find the critical angle of a material, set the
angle of refraction to 90°
 So for light going from water to air:
n1sinθ1 = n2 sinθ2
1.33 sinθ1 = 1.0003 sin 90
θ1 = 48.7 °
Lenses
 We know light passing from one material to
another bends at the surface (refraction).
 What if we have a curved surface?
 Convex lens – thick in middle
(also called converging lens)
 Concave lens – thin in middle
(also called diverging lens)
Convex Lenses
 Light entering lens parallel to primary axis
converges to focal point (Converging Lens!)
+f
Concave Lens
 Light entering lens parallel to primary axis
diverges as if coming from focal point.
-f
Mathematical Relationships
 Same as for curved mirrors!
Two-Ray Diagrams
 To draw a ray diagram and locate the image,
three rays can be drawn. (Need two)
Convex Lenses
 Ray diagrams can explain why image
changes with object distance
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Object far away: inverted, small, real image
Object closer, but still outside focal point:
inverted, bigger, real image
Object really close, inside focal point: upright,
bigger, virtual image (-di)
Concave Lens
 No matter where object is placed, the image
produced is virtual, upright and on same side
of lens as focal point (- di)
Summing up
 Convex lenses have +f
 If do> f, then image is inverted, real and on
other side of lens (+di)
 If do< f, then image is upright, virtual and on
same side of lens (-di)
 Concave lenses have –f
 Images are always upright, virtual, smaller,
and on same side of lens (-di)