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1
Speed of Light 1
c
Earth
Moon
d
d = 240,000 mi
t = 2.58 s
c = ? mi/s
c = v = 2d/t
c = (2)(240,000 mi)/2.58 s
c = 186,000 mi/s
c = 3 x 108m/s
Speed of Light 2
How many round trips can a
beam of light make around
the earth in 1 second?
Earth
d
1, 10, 100, 1,000 ?
d = 8,000 mi
Distance traveled in 1s = 186,000 mi
r = 4,000 mi
v = 186,000 mi/s
C=2πr
1 round trip = 2 π r = 2(3.14)(4,000 mi)
# of trips = 186,000 mi/ 2(3.14)(4,000 mi)
# of trips = approximately 8
Speed of Light 3
c
Sun
Earth
d
d = 93,000,000 mi
c = v = d/t
t = d/c
c = 186,000 mi/s
t=?s
t = ? min
t = 93,000,000mi/186,000 mi/s
t = 500 s
t = (500 s)(1 min/60 s) = 8.3 min
Light Year 1
Star
Earth
d
A light year (ly) is the distance light travels in 1 year
t = 1 year
v = 186,000 mi/s
d = 1 ly = ? mi
(1yr)(365d/yr)(24h/d)(3,600s/h) = 31,536,000 s
d = v t = (186,000 mi/s)(31,536,000 s)
d = 5,870,000,000,000 mi = 5.87 trillion miles
1 light year = 5.87 trillion miles
Light Year 2
Star X
Earth
100 ly
Light leaves star X in the year 2008
It arrives at Earth in the year 2108
We are all dead
The light that we now observe from
star X left the star in the year 1908.
Faster than the Speed of Light
v=2c
Year 2006
Spaceship leaves
Earth traveling at 2c
Earth
Planet X
10 ly
Year 2011
Spaceship arrives
on Planet X.
Light from takeoff is
half way to Planet X.
Earth
))))) c
10 ly
Year 2016
Light from takeoff
arrives on Planet X.
Space traveler
watches his takeoff.
Planet X
))))) c
Earth
Planet X
10 ly
To travel into the future you would have to travel faster than the speed of light.
1
Periodic Waves
Crest

v
Periodic
Wave
Trough
f = frequency
f = waves/second
1wave/second = 1 Hertz
λ = wavelength λ = distance crest to crest λ is measured in meters
v = speed of the wave
v is measured in m/s
If v is constant,  = 1/f
v=f
As f increases,  decreases
As  increases, f decreases.
Sound Waves

v
What is the wavelength of middle C?
Speed of sound in air ≈
v=f
λ = v/f
1,100 ft/s
f = 256 Hz
335 m/s
λ = 1100/256
750 mi/h
λ = 4.30 ft
If f is doubled f = 512 Hz, what is the wavelength of the wave?
v=f
λ = v/f
λ = 1100/512
λ = 2.15 ft
When f is doubled, the wavelength is half as great?

Light waves
v
The speed of light, c, is constant in a vacuum
C=
186,000 mi/s
3.00 x 108 m/s
This is the speed of all electromagnetic waves in a vacuum.
What is the frequency of red light (λ = 6.5 x 10-7 m)?
f = v/λ
f = (3.00 x 108)/6.5 x 10-7)
f = 460,000,000,000,000 Hz
f = 4.6 x 1014 Hz
f = 460 trillion Hz
White Light
Wave Model & Color
v=f
For red f is low,  is long
For blue f is high,  is short
Color, frequency, and Wavelength
λ is larger
λ is smaller
f is lower
R
O
Y
E
D
R
A
N
G
E
E
Y
Y
O
W
G
R
E
E
N
B
L
U
E
I
I
N
D
I
G
O
V
I
O
L
E
T
f is higher
Maxwell’s Rainbow
Color Sensitivity of Human Eye
The visible region of the spectrum is of course of
particular interest to us. Figure 33-2 shows the
relative sensitivity of the human eye to light of
various wavelengths. The center of the visible
region is about 555 nm, which produces the
sensation that we call yellow-green
The limits of this visible spectrum are not well
defined because the eye-sensitivity curve
approaches the zero-sensitivity line
asymptotically at both long and short
wavelengths. If we take the limits, arbitrarily, as
the wavelengths at which eye sensitivity has
dropped to 1% of its maximum value, these limits
are about 430 and 690 nm; however, the eye can
detect electromagnetic waves somewhat beyond
these limits if they are intense enough.
Mixing of Colors
Primary Colors of Light
Red + Green = Yellow
Red + Blue = Violet
Red + Green + Blue = White
Light and Matter
1. Light can be absorbed by matter
2. Light can be reflected by matter
3. Light can be transmitted through matter
1
i
r
Reflection of Light
i = r
Regular Reflection
Mirror
Irregular Reflection
Rough Surface
Speed of Light in Matter
c
vx < c
vx
c/vx = constant
This constant is called n (index of refraction)
c/vx= n
For air vx approximately equals c
Therefore, for air, n = 1
Index of Refraction of Various Materials
The following substances are
listed in alphabetical order.
Arrange them in order of
value of index of refraction.
Remember, the higher the
index of refraction, the slower
the speed of light in that
substance:
Air
Diamond
Glass
water.
1. Air
n = 1.0
2. Water
n = 1.3
3. Glass
n = 1.5
4. Diamond n = 2.4
Index of Refraction of Various Materials 2
c = 3.0 x 108 m/s
nwater = 1.3
nglass = 1.5
ndiamond = 2.4
nx = c/vx
Sample Problem #1
Determine the speed of light in
each of these materials.
vx = c/nx
vwater = 3.0 x 108 m/s/1.3 = 2.3 x 108 m/s
vglass = 3.0 x 108 m/s/1.5 = 2.0 x 108 m/s
vdiamond = 3.0 x 108 m/s/2.4 = 1.25 x 108 m/s
Refraction of Light
Optical density of
material 2 is greater
than the optical
density of material 1
1 > 2
1
2
Light will always bend toward the normal (dashed line).
Total Internal Reflection
1
2
c
At some angle, C , all light is reflected back into the material.
Rays at angles > c are totally internally reflected
The greater the index of refraction, n, the greater C .
1
The Eye
The image is formed on the retina.
The image is inverted and real.
As the object distance varies, the lens of the
eye contracts or expands to change it’s focal
length so that the image always forms on the
retina.
Optical Instruments
Objective
Eyepiece
For a telescope, the focal length of the objective lens is large.
For a microscope, the focal length of the objective lens is small.
Refracting Telescope
Objective
The focal length of the objective lens is large.
1/f = 1/do + 1/di
1/f = 1/  + 1/di
Eyepiece
The object is at infinity.
1/f = 1/di
The image formed by the objective lens is at the focal point and is real.
The image formed by the eyepiece is virtual and magnified.
do ≈ 
di ≈ f
Microscope
Objective
Eyepiece
The focal length of the objective lens is small.
The object is very close to the objective lens.
The image formed by the objective lens is real.
The image formed by the eyepiece is virtual and magnified.
Microscopes & Telescopes
In a microscope, the focal length of the objective lens is small. Why?
Because the object must be very close to the objective lens.
In a telescope, the focal length of the objective lens is large. Why?
Because the object is very far from the objective lens.