Physics 1230: Light and Color
Chuck Rogers, [email protected]
Matt Heinemann, [email protected]
www.colorado.edu/physics/phys1230
HWK 7 is due TUESDAY 5PM.
Projects
The project topics and teams look good.
Progress reports are due this week (Friday).1
Physics 1230: Light and Color
Chuck Rogers, [email protected]
Matt Heinemann, [email protected]
www.colorado.edu/physics/phys1230
Lecture 10
Refraction, spherical lenses, ray tracing and
image formation.
2
Where are we at?
Unit 1: What is light?
Unit 2: Light as a wave
Unit 3: Color in nature and technology (light
sources and the spectrum)
Unit 4: Reflection
Unit 5: Refraction
Unit 6: Lenses
Unit 7: Eye and camera
Unit 8: Color perception
Unit 9: Visual perception, illusion, art
Unit 10: TBD
Last Time: Refraction…
… is the bending of light rays due to the slowing
of light in a medium.
PhET bending light
OR…
• Light travels in straight lines at speed “c”
• Unless it enters another material (in which
case it changes direction and slows down)
• Light of different colors bends different
amounts
Why does the light ray bend?
“Light slows down inside materials”: Light
waves travel more slowly when they are inside
stuff. That makes the light wave bend.
Material
Air
Water
Glass
Diamond
Ruby
Refractive
Index
1.0008
1.330
1.5
2.417
1.760
Index of refraction, n:
c
n
v
c
OR v 
n
Index of Refraction
If the wavelength in air is 500 nm, what will be the
wavelength inside glass? Assume the index of
refraction of glass is 1.5
A)
B)
C)
D)
500 nm
400 nm
750 nm
333 nm
Index of Refraction
If the wavelength in air is 500 nm, what will be the
wavelength inside glass? Assume the index of
refraction of glass is 1.5
A)
B)
C)
D)
500 nm
400 nm
750 nm
333 nm
n
c
vGLASS

VAC f
vGLASS
VAC
n
GLASS
VAC f

GLASS f
Wavefronts bend when hit slower medium
faster medium
slower medium
• Wavefronts illustrate peaks and troughs in wave
• Right part of the wavefront hits the medium first and
is slowed down first.
• Causes the wave to bend.
The observer will see the underwater part of
body being
a) Shorter than it really is;
b) Taller than it really is;
c) Of natural size;
The observer will see the underwater part of
body being
a) Shorter than it really is;
b) Taller than it really is;
c) Of natural size;
Feet look like they’re here
• If the critical angle condition is satisfied,
will the snorkler see the upper part of the
swimmer’s body?
a) Yes;
b) No.
Feet look like they’re here
Legs up and down!
Both “n” and speed varies with color
Called “dispersion”
Ordinary glass
color
(blue)
n (index of refraction)
1.523 (bent more)
(yellow)
1.517
(deep red)
1.514 (bent less)
13
Rainbow: Dispersion via water droplets
180 degree rainbow is possible. Double rainbow (woah!) is possible.
Both together is very rare.
14
Rainbow: Colors spread within the raindrop
Dispersion occurs
here during refraction
Reflections
white light
comes in
Raindrop
Dispersion occurs
here during refraction
A spectrum of
colors comes out
How we see a rainbow
big
raindrops
Sun
(behind you)
this ray not seen
these rays are seen
this ray not seen
16
Waterfall droplets create rainbows
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Refraction all the way through block
Refraction all the way through block
What was happening in Activity 8?
U2L05
20
PHET simulation
U2L05
21
Ray tracing
• First draw the normal to each surface
• Then start with how the light leaves the source and hits the first
surface, then the second surface, then leaves the block
• Where does the eye think it came from?
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Ray tracing
U2L05
23
Ray tracing
U2L05
24
Ray tracing
U2L05
25
Ray tracing
U2L05
26
Ray tracing
Sight line
Apparent
Position (below
actual position)
Virtual image
U2L05
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Where are we at?
Unit 1: What is light?
Unit 2: Light as a wave
Unit 3: Color in nature and technology (light
sources and the spectrum)
Unit 4: Reflection
Unit 5: Refraction
Unit 6: Lenses
Unit 7: Eye and camera
Unit 8: Color perception
Unit 9: Visual perception, illusion, art
Lenses
• Mirrors reflect light and do not transmit light –
glass coated with silver at back.
• Lenses are made of materials that transmit light,
e.g., glass.
Examples of lenses: eyeglass, amplifying glass,
reading glass, camera, ...
29
Concave
and
convex
lenses
Convex and concave lenses
• Each of the two surfaces
has a spherical shape.
• Light can penetrate
through the lenses and
bend at the air-lens
interface.
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Light (the red ray) enters (and exits!) a thin window
pane (with parallel edges)
Which ray continues the red ray?
A
B
C
D
Light (the red ray) enters (and exits!) a thin window
pane (with parallel edges)
Which ray continues the red ray?
A
B
C
D
But what if the sides are NOT parallel?
The ray bends which way:
A
B
C
But what if the sides are NOT parallel?
The ray bends which way:
A
B
C
We build lenses out of glass with non-parallel sides
Glass
If slabs aren’t parallel - lens
Glass
A
B
C
Which ray of light will have changed direction the most upon exiting
the glass?
We build lenses out of glass with non-parallel sides
Put film,
Retina here!
37
We build lenses out of glass with non-parallel sides
Put film,
Retina here!
•
•
•
Light rays bent towards each other… CONVERGING LENS.
The less parallel the two sides, the more the light ray changes
direction.
Rays from a single point, converge to a single point on the other
side of the lens (and then start diverging again).
38
Definition: Focal point
When light rays approach a lens, parallel to the
axis of a lens, they come to a focus at the focal
point.
Converging (convex) lens
Parallel light rays coming in from an object
PHET
http://www.colorado.edu/physics/phet/dev/ht
ml/optics-lab/1.0.0-dev.9/optics-lab_en.html
Converging (convex) lens
optical
axis
Focus
f
Light rays coming in parallel focus to a point, called the focal point
Light focusing properties of converging lens
a good light collector or solar oven; can also fry ants with sunlight (but
please don’t do that)
42
Light focusing properties of converging lens
The “backwards” light collector:
create a collimated light beam
43
Ray tracing with lenses
Ray tracing:
n=1
Rays entering
“slower” material
bend toward
normal
n>1
Rays entering
“faster” material
bend away from
normal
1. As long as ray stays in
same medium, it goes
straight.
2. At each interface to a
different medium,
calculate how it will
bend. Go back to 1.
This gets tedious!
44
Thin convex (converging) lens
}
focal length
If the glass surface is
nearly a section of a
sphere, it will FOCUS
parallel rays.
A THIN LENS is very thin
compared to the focal
length. Then we can
simplify the treatment with
THREE NEW RULES.
F
F
foci
45
Thin convex (converging) lens: Ray tracing rules
1) A ray parallel to the axis
is deflected through the
focus on the other side
2) A ray through the center
of the lens continues
undeviated
3) A ray coming from the
focus on one side goes
out parallel to the axis
on the other
}
focal length
1
2
3
F
3
F’
foci
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Ray tracing exercise
Come get some handouts!
Ray tracing
Where will this ray go?
foci (focuses?)
48
Ray
Ray Tracing
tracing
Where will this ray go?
Suppose it’s emitted
from this object
foci (focuses?)
49
Ray
Ray Tracing
tracing
We know where these 3 rays
go, using the simple ray rules
foci (focuses?)
50
Ray
Ray Tracing
tracing
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point
We know where these 3 rays
go, using the simple ray rules
foci (focuses?)
51
Ray tracing: Thin lens, object outside focus
See how the rays emerge
from this point (the image)?
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point (the image)
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Ray tracing: Thin lens, object outside focus
Amazing property of
this lens: all rays from
the tip of the arrow will
converge to the same
point (the image)
The Lens acts as our
“Magic Ray Machine”,
creating the rays to
produce an image.
Eye sees an image
here.
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Clicker question
In this case, the image is:
A) Virtual
B) Real
Eye sees an image
here.
54
Clicker question
In this case, the image is:
A) Virtual
B) Real
Real because the light rays really
go through the image. You can put
a screen there to see it.
Eye sees an image
here.
55
Good place for a break!
Demo and PHET
http://phet.colorado.edu/en/simulation/geometric-optics
Idea of magnification and focused image
Ray tracing exercise
Ray tracing a convex lens: object inside focus
59
Ray tracing a convex lens: object inside focus
The image appears larger (and farther away) than the object.
This is a magnifying glass.
(Remember: a magnifying glass is a convex lens.)
Aside: near-sighted people need concave/diverging lenses; can a marooned
myopic start a fire with his eye-glasses?
60
Converging/convex lens:
Near objects are magnified and upright.
Far objects are upside down and smaller
Far object
Near object
Magnifying glass
Thin concave (diverging) lens
Guess how this ray will be bent:
F
F’
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Thin concave (diverging) lens: Ray tracing rules
1) A ray parallel to the axis
is deflected as if it came
from the focus
2) A ray through the center
of the lens continues
undeviated
3) A ray aimed at the focus
on the other side comes
out parallel
1
2
3
F
F’
Ray might have to be extended
Difference between concave and convex rules
1
F
F’
(Rule 3, the backwards
version of rule 1, also differs)
1
F
F’
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Thin concave (diverging) lens image
F
F’
(A) Or (B):
The image is LEFT or RIGHT of the lens.
The image is REAL or VIRTUAL.
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Thin concave (diverging) lens image
F
F’
(A) Or (B):
The image is LEFT or RIGHT of the lens.
The image is REAL or VIRTUAL.
The image appears smaller (and closer) than the object.
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Take a long breath…
Ray tracing lets you predict
how lens images work.
It is not the only way… We
have a mathematical way to
do it too.