Physics 1230: Light and Color
Chuck Rogers, [email protected]
Matt Heinemann, [email protected]
www.colorado.edu/physics/phys1230
No lecture on Friday (tomorrow).
HWK 2 is due Friday at 5PM on D2L.
1
Physics 1230: Light and Color
Chuck Rogers, [email protected]
Matt Heinemann, [email protected]
www.colorado.edu/physics/phys1230
Lecture 3:
Using light rays (a model for light): Pinholes
and images, shadows.
Start the wave picture of light: Traveling
waves, their wavelength, period, frequency,
and speed.
2
True or False: I have used the
metric system
A) TRUE
B) FALSE
True or False: I am comfortable
with the metric system
A) TRUE
B) FALSE
3
“SI” units of measure
(the metric system)
•
•
•
•
Length: meters (m)
Time: seconds (s)
Velocity: meters/second (m/s)
Frequency: cycles per second or Hertz (Hz)
Hz has units 1/seconds
Always state the units for your answers!
4
I have used ‘scientific notation’
A) Yes
B) No
C) What?!
True or False: I am comfortable
with scientific notation.
A) TRUE
B) FALSE
5
Scientific notation – powers of 10
1,000 = 1.0 x 103
2,100,000 = 2.1 x 106
1/(1,000) = 0.001 = 10-3
0.1 = 10-1
1 = 100
10 = 101
Calculator notation: 2.1 x 106 = 2.1E6
6
Scientific notation – prefixes
m
m
n
milli = 10-3
micro = 10-6
nano = 10-9
k
M
G
T
kilo = 103
mega = 106
giga = 109
Tera = 1012
Common usage:
wavelength in mm, mm or nm
frequency in kHz, MHz, GHz or THz
7
What do we see here?
Leaves are great pinhole viewers
These are
images
• The sun
through
trees
• The sun through
trees during an
eclipse
DEFINITION: “IMAGE”
An image is where we see something that looks
like the object (but the object isn’t actually there).
Examples: This projection screen, image in a
mirror, pinhole image of sun
The object photographed with a pinhole camera
does not have to be self-luminous!
One of many rays of light shining on Alex
Pinhole Camera
blocked rays
image
Alex
How can less be more?
A pinhole camera works by blocking rays
You can make a pinhole camera.
Great project idea!!
http://www.photojazz.ws/2009/07/how-to-make-a-pinhole-camera
Good pinhole cameras have tiny apertures
What about when the “pinhole” gets too large?
This is on
HWK 2
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
RAYS CROSS AT PINHOLE!!
Pinhole
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
RAYS CROSS AT PINHOLE!!
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
RAYS CROSS AT PINHOLE!!
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
Finding an image by using rays is called ray tracing.
Trace rays from the object through the pinhole in the camera to
find the image rather than trusting your intuition!
Is the image of Alex smaller or
larger than the real Alex?
Is the image of Alex smaller or
larger than the real Alex?
a)Smaller
b)Larger
c)Same size
a)Smaller
b)Larger
c)Same size
So a pinhole image size depends on…
• The size of the camera
• How far away the object is
• How big the object is
So a pinhole image size depends on…
• The size of the camera
• How far away the object is
• How big the object is
Breathe in… Breathe out…
QUESTIONS!!
Shadows
Sketch how the person’s shadow would appear. Use ray diagrams.
Shadows
Sketch how the person’s shadow would appear. Use ray diagrams.
Sun radiates
many rays
Shadows
Sketch how the person’s shadow would appear. Use ray diagrams.
Sun radiates
many rays
Some special rays
that tell a story
Shadows
Sketch how the person’s shadow would appear. Use ray diagrams.
Sun radiates
many rays
No rays
are blocked
(bright)
Some special rays
that tell a story
Some rays
are blocked
(dark)
No rays
are blocked
(bright)
Far away sun
Shadows: quantitative analysis of height
Far away sun
Shadows: quantitative analysis of height
Hb
Lb
Far away sun
Shadows: quantitative analysis of height
Hb
hh
Lb
lh
Far away sun
Shadows: quantitative analysis of height
What is special about these triangles?
A) They are exactly the same
B) They are isosceles
C) They are equilateral
D) They are similar
E) None of these
Hb
hh
Lb
lh
Far away sun
Shadows: quantitative analysis of height
What is special about these triangles?
They are similar. SO:
H B hh

LB
lh
HB
hh
LB
lh
What makes shadow sharp or “fuzzy”?
Some shadows like those above can be very crisp.
Can you make a sharp shadow on your
desk in this room? Why or why not?
Try It!
Can you make a sharp shadow on your
desk in this room? Why or why not?
A) YES
B) NO
Why or why not? THOUGHTS??
Language for more complex shadows:
Umbra and Penumbra
Umbra = all light from source is blocked
Penumbra = Imperfect blockage of light
Complicated shadows come from:
Extended sources
Multiple sources
Recall: Extended sources can be thought of
as combination of many point sources –
think back to last activity
Complicated shadows come from:
Extended sources
Multiple sources
Recall: Extended sources can be thought of
as combination of many point sources –
think back to last activity
Shadows: Extended source
Sharp vs fuzzy shadow
• Observation: Depends upon distance to screen
Multiple ray model helps us understand this behavior
Object near wall:
Sharper shadow
Object near bulb:
fuzzier shadow
Shadows: Extended source
Sharp vs fuzzy shadow
• Observation: Depends upon distance to screen
Multiple ray model helps us understand this behavior
Object near wall:
Sharper shadow
Object near bulb:
fuzzier shadow
Shadows: Extended source
Sharp vs fuzzy shadow
• Observation: Depends upon distance to screen
Multiple ray model helps us understand this behavior
Object near wall:
Sharper shadow
Special rays
to help
Object near bulb:
fuzzier shadow
Shadows: Extended source
Sharp vs fuzzy shadow
• Observation: Depends upon distance to screen
Multiple ray model helps us understand this behavior
Object near wall:
Sharper shadow
Special rays
to help
penumbra
Umbra
penumbra
Object near bulb:
fuzzier shadow
Shadows: Extended source
Sharp vs fuzzy shadow
• Observation: Depends upon distance to screen
Multiple ray model helps us understand this behavior
Object near wall:
Sharper shadow
Special rays
to help
penumbra
Umbra
penumbra
Object near bulb:
fuzzier shadow
Shadows: Multiple light sources
Penumbra
Umbra
Separate shadow from each light
source
Overlapping shadows
Red/blue light shadows: Clickers
If I move the hand closer to the screen
A) the umbra will get larger compared
to penumbra
B) the penumbra will get larger
compared to umbra
C) little or no change in the shadow
Red/blue light shadows: Clickers
If I move the sources farther apart
A) the umbra will get larger compared
to penumbra
B) the penumbra will get larger
compared to umbra
C) little change in the shadow
Generally speaking…
• The size of the shadow can be predicted by ray
diagrams (proportional to height).
• Sharp shadows from:
• Smaller, pointlike light sources (the sun far away looks
“pointlike” to us)
• Small distance between the object, and what it casts a
shadow on
• But you can predict a particular situation with ray
diagrams!
Spectacular shadows:
Solar eclipse (moon shadowing sun)
Sun
Moon
Earth
Where would an observer need to stand in order to see
the total eclipse of the sun?
A) Umbra B) Penumbra C) On the moon
(B) umbra only few 100 km
(A) Penumbra much larger
umbra only few 100 km
Good place for a break!
What is light?
50
What is light?
Ray model
Light travels as
rays in all
directions
Rays from point source
51
What is light?
Ray model
Light travels as
rays in all
directions
Wave model
Light travels as
a wave.
Rays from point source
Waves from point source52
What is light?
Ray model
Light travels as
rays in all
directions
Wave model
Light travels as
a wave.
Rays from point source
Waves from point source53
Waves on a rope
http://phet.colorado.edu/new/simulations/sims.php?sim=Wave_on_a_String
Wave basic properties
Wave repeats its shape each time you
move left or right by a special distance.
X
l
l is called the ‘wavelength’.
Wave basic properties
Wave travels at some speed.
X
l
l is called the ‘wavelength’.
c is the speed.
Wave basic properties
So, after some time, T, called the period,
the wave looks the same as initially.
X
l
l is called the ‘wavelength’.
c is the speed.
T is the period.
Wavelengths
nanometers
58
Visible spectrum
59
Frequency and Period
• Frequency is the number of
full cycles per second
• Period is the time to swing
forth and back
• If f = 2 Hz,
then 2 swings per second,
and period = 0.5 s.
60
Some radio wave frequencies
•
•
•
•
•
•
Submarine communication, 76 Hz
AM radio, 520 – 1610 kHz
FM radio, 87.5 – 108 MHz
Wireless internet, 2.4 GHz
GPS, 1575 MHz or 1.575 GHz
Security scanner: 1000 GHz = 1 THz
The frequency of light is very high, ~1015
Hz, and is off this scale.
61
Light is an oscillating E and B-field
• Oscillating ELECTRIC and magnetic field
• Traveling to the right at speed of light (c)
Electromagnetic
radiation
Snap shot of E-field in time:
At t=0
A little later in time
E
c
X
Function of position (x) and time (t):
E(x,t) = Emaxsin(ax+bt)
sin(ax-bt)
A good place to stop today…
HWK 2 is due tomorrow,
Friday at 5PM in the D2L
dropbox!
NO LECTURE TOMORROW OR OTHER FRIDAYS.
Enjoy the rest of your day.
See you Monday.