Lecture #3

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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.

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Lecture #3

What you see is what you get

1/31/13

Homework
• Problems up on web site
• Due next Tuesday
• Questions??
Today’s topics
• Reflection
• Absorption / Transmission
• Measuring fR, fA, and fT
• Spectral properties of light environments
• Terrestrial
• Aquatic
• 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

Itrans

Ireflect

θ1 = θ2 = 0

1. Reflection at interface
• Light will reflect at interface between materials with different indices of refraction
• For light perpendicular to

surface

n=1.0

Water n=1.33

• fR, fraction reflected

θ1 = θ2

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 and fR ≈ 0 so that
• fT + fA = 1 What does that mean???
Calculating transmission – solution of concentration, C
• Beer’s law

εdepends on what substance is

C is concentration

l is the pathlength

I0

I, light transmitted through

l

Calculating transmission - solution
• Beer’s law

ε depends on what substance is

C is concentration

l is the pathlength

I0

I0

I

I

Low concentration High concentration

Less absorbed More absorbed

More transmitted Less transmitted

Calculating transmission - solution
• Beer’s law

ε depends on what substance is

C is concentration

l is the pathlength

I0

I0

I

I

Short pathlength Longer pathlength

Less absorbed More absorbed

More transmitted Less transmitted

Calculating transmission - pure substance, like water
• Beer’s law

α is attenuation coefficient

I0

I

l

Units all cancel so take exponential of a unitless number
• ε length-1 concentration-1 = L-1 molecules-1L3

= L2/molecule

l length

C concentration = molecule / L3

• L-1
• 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 + fR + fA = 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

Measuring reflection / scattering

Fiber optic

Light source

Spectrometer

How can we measure I0?

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
• Q = I * R * S

Intensity

Reflectance

Q = quanta of light detected

What light illuminates an object?
• Light flux on a surface - from all directions
• Photons /s m2

• Light flux on a surface - from all directions
• Photons /s m2
• Light flux from a particular direction and angle
• Photons /s m2sr

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
Eyes respond to photons
• Eye doesn’t care about watts
• Chemical reactions in eye detect individual photons
How many photons in a Watt
• Watt is a measure of power = energy / time
• 1 watt = 1 J/s
• Convert watts to photons
Energy of a photon – thank Planck
• E = hf = h c / λ
• 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
Solar spectrum

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

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

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
• αλ – attenuation coefficient varies with wavelength
Why does α vary with wavelength?
• Water reflection depends on wavelength
• Water refraction depends on wavelength
• Water absorption depends on wavelength
• None of the above
Attenuation coefficient of pure water
• Which wavelength light is transmitted best?
• 350 nm
• 450 nm
• 550 nm
• 650 nm

α

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
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

Light penetration

“Blue” oceanic waters

Color of transmitted light

Color of water

Levine

Sci Am

1982

400 450 500 550 600 650 700 nm

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

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

10 m

50 m

0 m

25 m