Lecture #3
What you see is what you get
1/31/13
Homework
• Problems up on web site
• Due next Tuesday
• Questions??
What are organisms’ visual tasks?
Foraging
Finding / choosing mates
Avoiding predators
Knowing when to stop
What happens to light when we
see?
Today’s topics
1.
2.
3.
4.
5.
Reflection
Absorption / Transmission
Measuring fR, fA, and fT
Follow the photon’s path
Spectral properties of light environments
a. Terrestrial
b. Aquatic
c. Energy of a photon
Light interactions
• Matter will interact with light in one of 4
ways
Reflected
Absorbed
Transmitted = Refracted
Scattered
• For now we will deal with transparent
materials so scattering will be negligible
Light interactions
• Photons are conserved
Light going in must go somewhere
Iincident = ITrans + IReflect + Iabsorb = I0
• Express as fraction of I0
fT + fR + fA = 1
fT=fraction transmitted
fR=fraction reflected
fA=fraction absorbed
Iabsorb
I0
Ireflect
Itrans
1. Reflection at interface
• Light will reflect at interface between
materials with different indices of
refraction
• For light perpendicular to
surface
fR = fraction _ reflected
æ n2 - n1 ö
fR = ç
è n2 + n1 ÷ø
1 2 0
n=1.0
2
Water n=1.33
Reflection at biological interfaces is
usually pretty small: air / water
• fR, fraction reflected
2
fR,air-water
æ n2 - n1 ö æ 1.33 -1.0003 ö
=ç
=ç
= 0.02
÷
÷
è n2 + n1 ø è 1.33 +1.0003 ø
2
1 2
n=1.0
Water n=1.33
2. Absorption
• Light will interact with molecules in
material
It can excite molecules. If it matches
electron resonance, then it will be
absorbed
If not, it will be transmitted
• We see what is not absorbed
In the following, we assume…
• Reflection is pretty small
• Then fT + fR + fA = 1
that
fT + f A = 1
and fR ≈ 0 so
What does that mean???
Calculating transmission – solution of
concentration, C
• Beer’s law
I = I 0 exp(-e l Cl)
I0
I = I 0e
εdepends on what
substance is
C is concentration
l is the pathlength
I, light transmitted
through
- e Cl
l
Calculating transmission - solution
• Beer’s law
I = I 0 exp(-e l Cl)
I0
I
Low concentration
Less absorbed
More transmitted
 depends on what
substance is
C is concentration
l is the pathlength
I0
I
High concentration
More absorbed
Less transmitted
Calculating transmission - solution
• Beer’s law
I = I 0 exp(-e l Cl)
I0
I
Short pathlength
Less absorbed
More transmitted
 depends on what
substance is
C is concentration
l is the pathlength
I0
I
Longer pathlength
More absorbed
Less transmitted
Calculating transmission - pure
substance, like water
• Beer’s law
I = I 0 exp(-a l)
 is attenuation
coefficient
I0
I
l
Units all cancel so take exponential
of a unitless number
ε
l
C
 L-1
l L
length-1 concentration-1 = L-1 molecules-1L3
= L2/molecule
length
concentration = molecule / L3
Transmission / absorption depend on
wavelength
I
fT = = exp(-a l l)
I0
fA = 1- fT =1- exp(-a l l)
3. Measuring transmission /
absorption
Measure I0 - just beam
flashlight
Fiber optic
Spectrometer
Measuring transmission /absorption
Measure I with object in beam
flashlight
Fiber optic
Transmission = I / I0
fT + f R + f A = 1
For small fR
fA = 1-fT
Spectrometer
For reflective objects
Specular reflection
For opaque objects light scatters in
all directions
Specular reflection
Scattered
Reflected light vs scattered light
Scattering / reflection depend on
wavelength
• n depends on 
Measuring reflection / scattering
Fiber optic
Light
source
How can we measure I0?
Spectrometer
Measuring reflection / scattering
Fiber optic
Light
source
Spectrometer
Measure I0 of light
Use white target that reflects all wavelengths
Measuring reflection / scattering
Fiber optic
Light
source
Spectrometer
Measure I reflected from object
fRorS = I / I0
fRorS + fA + fT = 1 where reflection
and scattering depend on angle
For small fT
fRorS = 1 - fA
Examples of absorption and
reflection
• The return of the spectrometer
Why does absorption matter?
• Retinal pigments absorb certain
wavelengths
• Biological materials
- Photosynthesis uses light to power life
- Wavelengths scattered depend on
absorption
- Colors of animals, food
- Define our environment
4. The photon’s path - How do we see?
Sensitivity
• Light from a source, I
• Reflected by object, R
• Detected by eye, S
Intensity
• Q= I *R *S
Reflectance
Q = quanta of light detected
What light illuminates an object?
• Irradiance
Light flux on a
surface - from all
directions
Photons /s m2
Irradiance
Depending on detector set up, we might
measure irradiance or radiance
• Irradiance
Light flux on a
surface - from all
directions
Photons /s m2
Irradiance
• Radiance
Light flux from a
particular direction
and angle
Photons /s m2 sr
Radiance
Light measurement
• Many light meters measure watts / m2
Watts are joules / s and so are related to
photons / s
We’ll convert that in a minute
• Some light meters measure lux
This is like watts / m2 but they take human
sensitivity into account
Lux meter (measures irradiance – all
angles)
Bright sunlight
20,000 lux
Eyes respond to photons
• Eye doesn’t care about watts
• Chemical reactions in eye detect
individual photons
Energy of light source is given in
watts
75 W light bulb
5 mW laser
How many photons in a Watt
• Watt is a measure of power = energy / time
1 watt = 1 J/s
• Convert watts to photons
energy
energy
# photons
Lightsource _ power(W ) =
=
*
s
one _ photon
s
# photons Lightsource _ power(W )
=
s
energy / one _ photon
Energy of a photon – thank Planck
• E = hf = h c / 
h is Planck’s constant = 6.6256 x 10-34 Js
For 400 nm light:
E = (6.6256 x 10-34 Js) (2.998 x 108m/s)
400 x 10-9 m
E = 4.96 x 10-19J per photon
Energy of photon determines #photons/watt
Red laser
More photons per W at longer wavelength
Red laser
• Laser power is 3 mW at 650 nm
• # photons/s =
Power
energy per photon
=
0.003 W
3.0x10-19J/photon
= 9.8 x 1015 photons / s
5. Natural light sources
• Lots of variation in natural light
Light at high noon
Light at dawn, dusk
Light at midnight
Light in forest
Light at ocean surface
Light 100 m depth
• Illuminant shapes what we can see
Light environment : sky conditions
Light environment : sky conditions
Light environment : sky conditions
Environment : Lighting conditions
Light environment : Viewing angle
Light environment : time of day
Light environment : Time of day
Solar spectrum
1.2
Irradiance in watts / m2
Relative intensity
1.0
0.8
0.6
0.4
0.2
0.0
300
400
500
600
700
Wavelength (nm)
800
900
1000
Light spectrum in terms of photon
flux
Since there are more
photons per watt at
longer wavelengths, the
curve shape changes
when presented as
photons / m2 sec
Loew and
McFarland 1990
Compare spectra of sunlight and
moonlight
Why are they similar?
Why are they different?
Loew and
McFarland 1990
Light from sun versus moon
Moon
Sun
Earth
How does solar spectrum vary for
high noon vs dawn / dusk
Sun angle changes
with time of day
This changes
pathlength through
atmosphere
Dawn / dusk
Lose mid to long
wavelengths at dawn and
dusk
Loew and McFarland 1990
Fleishman et al. 1997
Here
are light spectra (irradiance) for forest habitats
Shade
Terrestrial habitats
Fleishman et al. 1997
Shade
Sun
Terrestrial habitats
Why is light in the forest
different?Absorption of light by
chlorophylls
Light reflecting off vegetation
Fleishman et al. 1997
Shade
Sun
Terrestrial habitats
Fleishman et al. 1997
Shade
Sun
Terrestrial habitats
Affects of the terrestrial environment
• Lighting and contrast with background
determines how easily you can be seen
Cryptic (camouflage) - blend in
Conspicuous - stand out
• Lighting and contrast with background
determines how easily your food can be
detected
Light under water
• Water attenuates certain wavelengths
more than others
I = I 0 exp(-a l l)
   – attenuation coefficient varies with
wavelength
Why does α vary with wavelength?
A) Water reflection depends on
wavelength
B) Water refraction depends on
wavelength
C) Water absorption depends on
wavelength
D) None of the above
Attenuation coefficient of pure water
1
0.8

K (m-1)
0.6
0.4
Which wavelength light is transmitted
best?
A) 350 nm
B) 450 nm
C) 550 nm
D) 650 nm
0.2
0
300
400
500
Wavelength
600
700
Light transmission of clear water
m
How can we calculate the light
spectrum underwater?
• We take the light spectrum at the waters
surface and
• Multiply it by the fraction of light that is
transmitted
Solar illumination at different depths
Incident
sunlight
m
Light penetration
“Blue”
oceanic
waters
Levine
Sci Am
1982
400
450
500
550
600
650
700 nm
Light penetration
“Blue”
oceanic
waters
Levine
Sci Am
1982
400
450
500
550
600
650
700 nm
Light penetration
“Blue”
oceanic
waters
Levine
Sci Am
1982
400
450
500
550
600
650
700 nm
Light at dawn / dusk in air or under water
Loew and McFarland 1990
Note photons/s not Watts
Decrease in light intensity with depth
1
Relative light intensity
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
50
100
150
Depth
200
250
Decrease in light intensity with depth
- log scale
1
0.1 0
200
400
600
0.01
Relative light intensity
0.001
0.0001
1E-05
1E-06
1E-07
1E-08
1E-09
1E-10
1E-11
Limit of human
sensitivity
1E-12
1E-13
1E-14
Depth
800
1000
Land &
Nilsson Table
2.1
Color of transmitted light
“Blue”
oceanic
waters
Levine
Sci Am
1982
400
450
500
550
600
650
700 nm
Color of water
Light penetration
Rivers and lakes can vary in water clarity
Different waters attenuate differently
1+2 open ocean
3 ocean with
chlorophyll
4 coastal waters
with chlorophyll
and dissolved
organics
“Fresh” water
“Green” river water
Swampy “red” waters
Which curve describes light
attenuation in Green River?
4
3
2
1
Aquatic environment
•
•
•
•
•
Depth
Habitat (coral reef vs ocean)
Camouflage - blending in
Light levels (especially in deep ocean)
Kind of water that you’re in
How light is transmitted / attenuated
FishBase: Fish at depth viewer
Amphiprion ocellaris
Amphiprion at depth
0m
10 m
25 m
50 m