Chapter 10 - Light
94
Light
Transcript of Chapter 10 - Light
Light
Light: Three models• Newton’s particle model (rays)
– Models light as bits of energy traveling very fast in straight lines.
• Huygens’s/Maxwell wave model– Models light at waves (transverse EM waves). Color
determined by frequency, intensity by square of a total oscillating amplitude.
• Einstein’s photon model– Models light as “wavicles” == quantum particles
whose energy is determined by frequency and that can interfere with themselves.
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Quantum Electrodynamics
Physical Optics (Wave model)
Geometric Optics (Ray model)
Einstein’s photon model
Venn Diagram
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Modeling in Biology
Are there examples in biology where you also need different models ?
Each model highlights different properties of the protein- Hydrophobic character- Folding property
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Reason for multiple models
• Each “model” of light highlights a particular characteristic of light (just like each model of a protein highlights a particular aspect of what proteins are and how they work)
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Light: Purpose of the three models• Newton’s particle model (rays)
– Models how light interacts with mirrors and lenses
• Huygens’s/Maxwell wave model– Models cancellation and interference
• Einstein’s photon model– Models absorption and emission of light
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The Ray Model
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Classical Electromagnetism - Maxwell’s Equations
Charge density
Current density
Everything in models (1) and (2) is contained in Maxwell’s Equations
You are not expected to know these. Just know they exist.
𝛻𝛻 � 𝐄𝐄 =𝜌𝜌𝜖𝜖0
𝛻𝛻 × 𝐄𝐄 = −𝜕𝜕𝐁𝐁𝜕𝜕𝜕𝜕
𝛻𝛻 � 𝐁𝐁 = 0
𝛻𝛻 × 𝐁𝐁 = 𝜇𝜇0 �⃑�𝑱 + 𝜖𝜖0𝜕𝜕𝐄𝐄𝜕𝜕𝜕𝜕
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Electromagnetic Waves are one type of solution to Maxwell’s equations
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Special Case Sinusoidal Waves
Wavenumber and wavelength
These two contain the same information
𝑘𝑘 =2𝜋𝜋λ
λ =2𝜋𝜋𝑘𝑘
Ey (x, t) = f+ (x - vemt) = E0 cos k(x - vemt)[ ]
Ey (x, t)
E0
- E0
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Special Case Sinusoidal Waves
Introduce
Different ways of saying the same thing:
2𝜋𝜋 = 𝑘𝑘𝑣𝑣𝑒𝑒𝑒𝑒𝑇𝑇
𝜔𝜔 =2𝜋𝜋𝑇𝑇
𝑓𝑓 =1𝑇𝑇
𝜔𝜔𝑘𝑘
= 𝑣𝑣𝑒𝑒𝑒𝑒 𝑓𝑓λ = 𝑣𝑣𝑒𝑒𝑒𝑒
Ey (x, t) = f+ (x - vemt) = E0 cos k(x - vemt)[ ]
Ey (x, t)
E0
- E0
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Polarizations
We picked this combination of fields: Ey - Bz
Could have picked this combination of fields: Ez - By
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Waves emanating from a point source
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Motion of crests
Direction of power flow
When can one consider waves to be like particles following a trajectory?
Wave crests
• Wave model: study solution of Maxwell equations.Most complete classical description. Called physical optics.
• Ray model: approximate propagation of light as that of particles following specific paths or “rays”. Called geometric optics.
• Quantum optics: Light actually comes in chunks called photons
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What is the difference?Diffraction.
Comparable to opening size
Much smaller than opening size
λ λ
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Diffraction
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Chapter 23 Preview
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In the Ray Picture a beam of light is a bundle of parallel traveling rays
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Foothold Ideas 1:Light as Rays - The Physics
• Through empty space (or ~air) light travels in straight lines.
• Each point on an object scatters light, spraying it off in all directions.
• A polished surface reflects rays back again according to the rule: The angle of incidence equals the angle of reflection.
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Foothold Ideas 2:Light as Rays - the perception
• We only see something when light coming from it enters our eyes.
• Our eyes identify a point as being on an object when rays traced back converge at that point.
Light travels through a transparent material in straight lines called light rays.
The speed of light is v = c/n,where n is the index of refraction of the material.
Light rays do not interact with each other.
Two rays can cross without either being affected in any way.
The Ray Model of Light
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Light interacts with matter in four different ways:At an interface between two materials, light can be either reflected or refracted.Within a material, light can be either scattered or absorbed.
The Ray Model of Light
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An object is a source of light rays. Rays originate from every point on the
object, and each point sends rays in all directions.
The eye “sees” an object when diverging bundles of rays from each point on the object enter the pupil and are focused to an image on the retina.
The Ray Model of Light
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Objects can be either self-luminous, such as the sun, flames, and lightbulbs, or reflective.
Most objects are reflective.
Objects
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The diverging rays from a point source are emitted in all directions.
Each point on an object is a point source of light rays. A parallel bundle of rays could be a laser beam, or
light from a distant object.
Objects
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Rays originate from every point on an object and travel outward in all directions, but a diagram trying to show all these rays would be messy and confusing.
To simplify the picture, we use a ray diagram showing only a few rays.
Ray Diagrams
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A camera obscura is a darkened room with a single, small hole, called an aperture.
The geometry of the rays causes the image to be upside down.
The object and image heights are related by:
Apertures
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We can apply the ray model to more complex apertures, such as the L-shaped aperture below.
Apertures
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A. AB. BC. C
The image part with relationship ID rId7 was not found in the file.
A B C
21%27%
51%
The dark screen has a small hole, ≈2 mm in diameter. The lightbulb is the only source of light. What do you see on the viewing screen?
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A B C D E
0% 0% 0%0%0%
Two point sources of light illuminate a narrow vertical aperture in a dark screen. What do you see on the viewing screen?
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Suppose you have a small brightly lit bulb, a mask (a cardboard screen with a small circular hole cut in it), and a screen. You see a small circle of light on the screen. What would happen to the spot if you moved the bulb straight upward a bit?
A. The spot would stay where it was.B. The spot would move up a bit.C. The spot would move down a bit.D. The spot would move right a bit.E. The spot would move left a bit.F. Something else would happen.
The s
pot would st
ay w
here i..
.
The s
pot would m
ove up a bit.
The s
pot would m
ove down ...
The s
pot would m
ove rig
ht a ...
The s
pot would m
ove le
ft a bit.
Something e
lse w
ould happen
.
0% 0% 0%0%0%
100%
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Suppose you have two lit bulbs, the top one red and the bottom one blue, a mask (a cardboard screen with a small circular hole cut in it), and a screen, as shown.
What would you see on the screen if you held the bulbs one over the other as shown?
A. One purple circle.B. Two circles, one above the
other with the top one red, the lower one blue.
C. Two circles, one above the other with the top one blue, the lower one red.
D. Something else.
One purple cir
cle.
Two cir
cles, o
ne above th
e ...
Two cir
cles, o
ne above th
e ...
Something e
lse.
17%7%
67%
9%
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Kinds of Images: Real• In the case of the previous slide, the rays
seen by the eye do in fact converge at a point.• When the rays seen by the eye do meet,
the image is called real.• If a screen is put at the real image, the rays
will scatter in all directions and an image can be seen on the screen, just as if it were a real object.
When I arrived in New York for the first time, we flew low over
Manhattan and I was impressed with the view of the city lights in the dark. Being tired after a long flight, I tried
to take a picture through the window using my flash. Explain why this is a bad idea and what the picture was
likely to show.
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Chapter 23 Preview
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Foothold Ideas 3:Mirrors
• For most objects, light scatters in all directions. For some objects (mirrors) light scatters from them in controlled directions.
• A polished surface reflects rays back again according to the rule: The angle of incidence equals the angle of reflection.
mirrorordinary object
𝜃𝜃𝑖𝑖 𝜃𝜃𝑟𝑟
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Where does an object seen in a mirror appear to be?
object
Virtualimage of theobject
equal distancealong perpendicular
Light rays do not carry information on whether they were reflected!
An observer O, facing a mirror, observes a light source S. Where does O perceive
the mirror image of S to be located?
A. 1B. 2C. 3D. 4E. Some other locationF. O cannot see S in the
mirror when they are as shown.
1 2 3 4
Some oth
er locat
ion
O cannot s
ee S
in the m
irro...
10% 10%
2%2%
55%
22%
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Kinds of Images: Virtual• In the case of the previous slide, the rays
seen by the eye do not actually meet at a point – but the brain, only knowing the direction of the ray, assumes it came directly form an object.
• When the rays seen by the eye do not meet, but the brain assumes they do, the image is called virtual.
• If a screen is put at the position of the virtual image, there are no rays there so nothing will be seen on the screen.
I have a small mirror – about 8 inches high – hanging on my wall. When I’m standing right in front of it, I can only see my head. Can I see all of myself at once by moving far back enough?
1. Yes2. No3. I can if I …
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Reflection from a flat, smooth surface, such as a mirror or a piece of polished metal, is called specular reflection.
Specular Reflection of Light
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The law of reflection states that:1. The incident ray and the reflected ray are in the same
plane normal to the surface, and2. The angle of reflection equals the angle of incidence:
θr = θI
Reflection
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Example 23.1 Light Reflecting from a MirrorWhiteboard, TA
& LA
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Example 23.1 Light Reflecting from a Mirror
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Example 23.1 Light Reflecting from a Mirror
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Most objects are seen by virtue of their reflected light. For a “rough” surface, the law of reflection is obeyed
at each point but the irregularities of the surface cause the reflected rays to leave in many random directions.
This situation is called diffuse reflection.
It is how you see this slide, the wall, your hand, your friend, and so on.
Diffuse Reflection
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Consider P, a source of rays which reflect from a mirror. The reflected rays appear to emanate from P′, the same
distance behind the mirror as P is in front of the mirror. That is, s′ = s.
The Plane Mirror
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The Plane Mirror
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You are looking at the image of a pencil in a mirror. What do you see in the mirror if the top half of the mirror is covered with a piece of dark paper?A. The full image of the
pencil.B. The top half only of the
pencil.C. The bottom half only of
the pencil.D. No pencil, only the paper.
The f
ull imag
e of the p
encil
.
The t
op half only
of the pencil.
The b
ottom half
only of t
he...
No pencil, o
nly the paper.
10%
34%34%
21%
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1. (3 pts) If we start our beaded string off in a sinusoidal shape y(x) = A sin(πx/L) it will oscillate with a period T0. If we start it out with a shape y(x) = A sin(2πx/L) with what period will it oscillate?
A. T0B. 2T0C. T0/2D. Something else
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2.1 (2 pts) A tightly stretched string is oscillating as a function of time. Graph A is a graph of the string's shape at a particular instant of time and graph B is a graph of the string's velocity as a function of position at that same instant. (The vertical axis is greatly magnified.) Is the wave on the string a:
A.right going traveling waveB.left going traveling waveC.part of a standing wave growing in
amplitude at time t1D.part of a standing wave shrinking
in amplitude at time t1E.None of the above.F.You can’t tell from the info given.
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2.2 (2 pts) Same situation as 2.1 but now graph A is a graph of the string's velocity as a function of position at a particular instant of time and graph B is a graph of the string's shape at that same instant.Is the wave on the string a:
A.right going traveling waveB.left going traveling waveC.part of a standing wave growing in
amplitude at time t1D.part of a standing wave shrinking
in amplitude at time t1E.None of the above.F.You can’t tell from the info given.
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3. (3 pts) A wire is rigidly attached to a wall. A pulse is sent along the string toward the wall. What will happen when the pulse reaches the wall? If there is more than one answer, place them all in the box. If none of these will occur, put N in the box.
A. The entire pulse will travel in the wall.B. Some of the pulse will travel in the wall.C. Some of the pulse were reflect right-side-up.D. Some of the pulse will reflect upside-down.E. The entire pulse will reflect right-side-upF. The entire pulse will reflect upside-down
You want to put a “full length mirror” on the wall of your room; that is,
a mirror that is large enough so that you can see your whole self in it all at the same time.
How big should the mirror be? A. You can see yourself in any size
mirror if you go back far enough.B. It depends on the size of your room
and whether you can step back far enough from the mirror.
C. The mirror needs to be about half your size.
D. The mirror needs to be as big as you are.
E. Some other answer
You can se
e yourse
lf in an
y ...
It dep
ends on th
e size o
f you...
The m
irror n
eeds t
o be abou...
The m
irror n
eeds t
o be as big...
Some oth
er an
swer
27%
44%
2%2%
25%
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Example 23.2 How High Is the Mirror?
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Example 23.2 How High Is the Mirror?
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Example 23.2 How High Is the Mirror?
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Example 23.2 How High Is the Mirror?
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What does a mirror do to an image?
A. Flips it left to rightB. Flips it upside downC. Does bothD. Does something else
Flips it
left
to right
Flips it
upside d
own
Does both
Does so
mething e
lse
25% 25%25%25%
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Chapter 23 Preview
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Chapter 23 Preview
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Two things happen when a light ray is incident on a smooth boundary between two transparent materials:1. Part of the light reflects
from the boundary, obeying the law of reflection.
2. Part of the light continues into the second medium. The transmission of light from one medium to another, but with a change in direction, is called refraction.
Refraction
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Refraction
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Refraction
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Indices of Refraction
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When a ray is transmitted into a material with a higher index of refraction, it bends toward the normal.
When a ray is transmitted into a material with a lower index of refraction, it bends away from the normal.
Refraction
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A laser beam passing from medium 1 to medium 2 is refracted as shown. Which is true?
A. n1 < n2.B. n1 > n2.C. There’s not enough
information to compare n1 and n2.
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n1 < n2.
n1 > n2.
There
’s not e
nough in
forma..
.
33%33%33%
Tactics: Analyzing Refraction
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Example 23.4 Measuring the Index of Refraction
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Whiteboard, TA & LA
Example 23.4 Measuring the Index of Refraction
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Example 23.4 Measuring the Index of Refraction
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n1 = 1.59
ASSESS Referring to the indices of refraction in Table 23.1, we see that the prism is made of plastic.
Example 23.4 Measuring the Index of Refraction
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When a ray crosses a boundary into a material with a lower index of refraction, it bends away from the normal.
As the angle θ1 increases, the refraction angle θ2 approaches 90°, and the fraction of the light energy transmitted decreases while the fraction reflected increases.
The critical angle of incidence occurs when θ2 = 90°:
The refracted light vanishes at the critical angle and the reflection becomes 100% for any angle θ1 > θc.
Total Internal Reflection
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Total Internal Reflection
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A laser beam undergoes two refractions plus total internal reflection at the interface between medium 2 and medium 3. Which is true?
A. n1 < n3.B. n1 > n3.C. There’s not enough
information to compare n1 and n3.
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n1 < n3.
n1 > n3.
There
’s not e
nough in
forma..
.
33%33%33%
The most important modern application of total internal reflection (TIR) is optical fibers.
Light rays enter the glass fiber, then impinge on the inside wall of the glass at an angle above the critical angle, so they undergo TIR and remain inside the glass.
The light continues to “bounce” its way down the tube as if it were inside a pipe.
Fiber Optics
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In a practical optical fiber, a small-diameter glass core is surrounded by a layer of glass cladding.
The glasses used for the core and the cladding have:ncore > ncladding
Fiber Optics
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If you see a fish that appears to be swimming close to the front window of the aquarium, but then look through the side of the aquarium, you’ll find that the fish is actually farther from the window than you thought.
Image Formation by Refraction
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Rays emerge from a material with n1 > n2.
Consider only paraxial rays, for which θ1 and θ2 are quite small.
In this case:
where s is the object distance and s′ is the image distance.
Image Formation by Refraction
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A fish in an aquarium with flat sides looks out at a hungry cat. To the fish, the distance to the cat appears to beA. less than the actual distance.B. equal to the actual distance.C. greater than the actual distance.
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less t
han th
e actual
distance.
equal to th
e actual
distance.
greate
r than
the ac
tual dist
a...
33%33%33%
A prism disperses white light into various colors. When a particular color of light enters a prism, its
color does not change.
Color and Dispersion
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Different colors are associated with light of different wavelengths.
The longest wavelengths are perceived as red light and the shortest as violet light.
What we perceive as white light is a mixture of all colors.
Color
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The slight variation of index of refraction with wavelength is known as dispersion.
Shown is the dispersion curves of two common glasses.
Notice that n is larger when the wavelength is shorter, thus violet light refracts more than red light.
Dispersion
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One of the most interesting sources of color in nature is the rainbow.
The basic cause of the rainbow is a combination of refraction, reflection, and dispersion.
Rainbows
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A ray of red light reaching your eye comes from a drop higher in the sky than a ray of violet light.
You have to look higher in the sky to see the red light than to see the violet light.
Rainbows
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A narrow beam of white light is incident at an angle on a piece of flint glass. As the light refracts into the glass,
A. It forms a slightly diverging cone with red rays on top, violet rays on the bottom.
B. It forms a slightly diverging cone with violet rays on top, red rays on the bottom.
C. It remains a narrow beam of white light because all the colors of white were already traveling in the same direction.
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It form
s a sli
ghtly dive
rging .
..
It form
s a sli
ghtly dive
rging .
..
It rem
ains a
narrow bea
m of...
33%33%33%
Green glass is green because it absorbs any light that is “not green.”
If a green filter and a red filter are overlapped, no light gets through.
The green filter transmits only green light, which is then absorbed by the red filter because it is “not red.”
Colored Filters and Colored Objects
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The figure below shows the absorption curve of chlorophyll, which is essential for photosynthesis in green plants.
The chemical reactions of photosynthesis absorb red light and blue/violet light from sunlight and puts it to use.
When you look at the green leaves on a tree, you’re seeing the light that was reflected because it wasn’tneeded for photosynthesis.
Colored Filters and Colored Objects
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Light can scatter from small particles that are suspended in a medium.
Rayleigh scattering from atoms and molecules depends inversely on the fourth power of the wavelength:
Light Scattering: Blue Skies and Red Sunsets
Iscattered ∝λ4
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Light Scattering: Blue Skies and Red Sunsets
Sunsets are red because all the blue light has scattered as the sunlight passes through the atmosphere.
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