Physics 1230: Light and Color
Ivan I. Smalyukh, Instructor
Office: Gamow Tower, F-521
Email:
ivan.smalyukh@colorado.edu
Phone: 303-492-7277
Lectures:
Tuesdays & Thursdays,
3:30 PM - 4:45 PM
Office hours:
Mondays & Fridays,
3:30 PM – 4:30 PM
TA: Jhih-An Yang
jhihan.yang@colorado.edu
Class # 6
Physics 1230: Light and Color
Lecture 6:
Reading: Finish Chapter 2
HW due today;
New HW assigned (due in 2 weeks);
2
Chapter 2 – Geometrical Optics
Geometrical optics is the theory of RAYS (straight lines)
and how they reflect and refract (bend). Lots of similarity
to GEOMETRY of lines and triangles.
Main Topics
We
are
here
1.
2.
3.
4.
Shadows
Reflection
Refraction
Dispersion
3
Chapter 2 – Geometrical Optics
We
are
here
1. Shadows
2. Reflection
a)
b)
c)
a.
b.
c.
d.
Point source or diffuse source
Umbra and penumbra
How tall is my shadow?
Pinhole camera
Specular or diffuse
Equal angle rule
Mirror images, ray tracing
3. Refraction
4. Dispersion
4
What can happen to incoming
light
Transmitted
Glass
Reflected (including scattering)
Silver,
water
absorbed
Black
pavement
Or any partial combination of these things
Specular or diffuse?
Diffuse reflection
(paper)
Specular reflection
(mirror)
Diffuse transmission
(wax paper)
6
Equal angle rule (specular reflection)
qi = angle of incidence
qr = angle of reflection
qi = qr
qi
Incident Ray
is specular reflection
qr
Reflected Ray
Normal
Mirror
A normal is a line
perpendicular to
the surface.
7
Metals with mobile electrons can cancel out the
light field in forward direction - only reflection
• Metals reflect all waves below
a certain frequency
Plasma frequency of silver
• This plasma frequency
Plasma frequency of gold
varies from metal to
metal
• Silver reflects light waves at
all visible frequencies
• Gold and copper have a
yellow-brownish color
because they reflect greens,
yellows and reds but not
blues or violets
Plasma frequency of copper
What is a mirror?
• Since silver is such a good reflector a coating of silver on
glass - a good (common) mirror
• If the silver coating is thin enough the mirror can be made
to transmit 50% of the light and to reflect the other 50%
– This is called a half-silvered mirror
– A half-silvered mirror used with proper lighting can
show objects on one side or the other of the mirror
Law of specular reflection of a
ray from a mirror
• The ray from the light bulb is
diffusely reflected off chin. We
show one of the many rays
coming off his chin hitting a
mirror.
•
The incident ray undergoes
specular reflection off the mirror
Normal
This angle
= this angle
Mirror
– Note the reflected ray
•
Draw the normal to the mirror
– The angle of incidence = the angle
of reflection
The normal to the mirror is an imaginary
line drawn perpendicular to it from where
the incident ray hits the mirror
How is an image produced in a mirror?
Part 1: Ray-tracing
• To find out how Bob "sees"
Alex by looking in the mirror
we trace rays which obey the
law of reflection
Bob looks at
Alex's image
Alex
Mirror
The psychology of image interpretation
• We interpret all rays coming
into our eye as traveling from
a fictitious image in a straight
line to our eye even if they are
reflected rays!
• Example: To find the location
of his hair in the virtual image we
extend any reflected ray from hair
backwards
Bob looks at
Alex's image
Alex
Mirror
The meaning of a virtual image
• If we trace rays for every ray
from every part of Alex which
reflects in the mirror
– we get a virtual image of
the real Alex behind the
mirror.
– Alex's virtual image is the
same size as the real Alex
Bob looks at
Alex's image
Alex
Mirror
Bob sees Alex's image
in the same place when
he moves his head
Virtual image of Alex
is behind mirror
Let’s look at specular reflection
Ray reflection practice
retroreflector
Retroreflectors
• Bike reflectors
• Roadside reflectors
• Measuring distance to moon?
Half-silvered mirror
If the silver coating is thin enough the mirror can be made
to transmit 50% of the light and to reflect the other 50%
This is called a half-silvered mirror
A half-silvered mirror used with proper
lighting can show objects on one side or the
other of the mirror
Glass is like a 4% silvered mirror
Image in a mirror
1. If a point on the object is distance X in front of the
mirror, the same point in the image appears to be
distance X in back of the mirror, or Xobject = Ximage.
2. The image point is on the normal (extended) from the
object to the mirror.
Mirror
normal
extended
Xobject
Ximage
18
Ray tracing: Draw the image, then the rays
First: draw rays from image to eyes
Viewed from the side.
Mirror
Xobject
Ximage
19
Ray tracing: Draw the image, then the rays
First: draw rays from image to eyes
Second: draw rays from mirror to object
Mirror
Xobject
Ximage
qi = qr happens automatically using this method.
Demo on board
20
Right side up image?
The top ray goes to the top of the bottle.
It is right side up.
Mirror
Xobject
Ximage
qi = qr happens automatically using this method.
21
Right side up image?
The top ray goes to the bottom of the bottle.
It is upside down.
Xobject
Extension
Mirror
(to do this drawing,
the mirror must be extended)
Ximage
qi = qr happens automatically using this method.
22
Bottle on its side
Viewed from the side.
Mirror
(to do this drawing,
the mirror must be extended)
qi = qr happens automatically using this method.
23
For simple (flat) mirrors the image location is
therefore predictable without knowing where the
observer's eye is and without ray-tracing
Mirror
Mirror
Mirror
Mirror
Periscope
The image of the
bottle in the lower
mirror is:
A)Inverted
B)Not inverted
C)Something else
mirror
Original
OBJECT
mirror
25
Periscope?
extension
The first IMAGE
Original
OBJECT
26
Periscope?
extension
The second IMAGE
27
Periscope?
The image of the
bottle in the lower
mirror is:
A)Inverted
B)Not inverted
C)Something else
28
Multiple mirrors - a virtual image can act as a
real object and have its own virtual image
• Question: Where are
the images of Alex
in the 2 mirrors?
a)
b)
c)
d)
e)
Alex
At A only
At B only
At A and B only
At C only
At A, B and C
The virtual image at A acts as
an object to produce the virtual
image of C. It acts as an
intermediate image. More
precisely it is the red rays
which reflect as green rays.
Mirror
B
Mirror
A
C
Is the writing reversed?
AR
(Two mirrors, viewed from above)
A) YES
B) NO
30
AR
Is the writing reversed?
31
ЯA
Is the writing reversed?
AR
AR
extension
ЯA
32
Is the writing reversed?
AR
AR
A) YES
B) NO
ЯA
33
Lec. 6: Ch. 2 - Geometrical Optics
We
are
here
1.
2.
3.
4.
Shadows
Reflection
Refraction
Dispersion
34
Refraction
1.
2.
3.
4.
Index of refraction: n = c / v
Ray in water is closer to the normal
Total internal reflection
Mirages
35
Reflection of waves occurs where the
medium of propagation changes abruptly
• Part of the wave can be
transmitted into the second
medium while part is reflected
back
• When light waves are incident
on a glass slab they are mostly
transmitted but partly reflected
(about 4%)!
– You can hear someone from
outside the pool when you are
underwater because sound
waves are transmitted from the
air through the water (with
different speed in each).
Glass slab
Is the speed of light in the glass slab the same as in the free space???
No.
How can reflection require that the speed of the wave
changes? We thought the speed of light was always
c = 3 x 108 m/s!
• The speed of an electromagnetic
• Light is reflected and
(EM) wave is constant (for every
transmitted at a boundary
wavelength) in empty space!
because
• The speed of light is slower than c
– When a light wave travels in a
in glass, water and other
medium the electric field of the
transparent media
– (Einstein showed that light can
never travel faster than c)
• The speed of light in a medium is
v = c/n, where n is a number
larger than one called the index of
refraction
• n = 1.5 for glass
• n = 1.3 for water
• n = 1.5 for vegetable oil
light jiggles the electrons in the
medium.
– This produces new electric
fields which can cancel or add
to the original light wave both
in the forward and backward
directions
• These are the transmitted and
reflected light waves
Refractive indices of different materials
Material
Refractive Index
Air
1.0008
Water
1.330
Glass
1.5
Diamond
2.417
Ruby
1.760
Oil
1.5
Can we see a glass rod immersed
into the oil with the same
refractive index?
• A. Yes
• B. No
Demo
Got to here on Thursday 6/10/2010
Refraction is the bending of a ray after it
enters a medium where its speed is different
•
A ray going from a fast medium to a
slow medium bends towards the normal
Air (fast medium)
Normal
to the surface of the medium
• A ray going from a slow medium to a
fast medium bends away from the
Glass or
normal to the surface of the medium
water
• The speed of light in a medium is v =
nair < nwater
(slow)
c/n, where n is a number larger than one
1.0008 < 1.33
called the index of refraction and
c = 3 x 108 m/s
• n = 1.3 for glass
Normal Air (fast medium)
• n = 1.5 for water
• Hence, a ray going into a medium with
a higher index of refraction bends
Glass or
towards the normal and a ray going
water
into a medium with a lower index of
(slow)
refraction bends away from the normal
How about light going into a medium with exactly the same index of refraction?
Ray-bending together with our psychological straight-ray
interpretation determine the location of images underwater
• The precise amount of bending
is determined by the law of
refraction (sometimes called
Snell's law):
•
ni sinqi = nt sinqt
• Here, qi = angle between incident
ray and normal,
• and qt = angle between transmitted
ray and normal
• ni and nt are the indices of
refraction in the medium
containing the incident ray and in
the medium containing the
transmitted ray
• Fig 2.49 Fisherman and fish
normal
transmitted
ray
image of fish for
someone out of water
incident
ray
fish
• In order to observe the fish from outside the
water a transmitted ray must enter your eye.
• You will think it comes from a point obtained by
tracing it backwards,
• Extend any 2 of the many many transmitted
rays from the fish backwards to find the image of
the fish (where they intersect).
• The location of that image will be the same for
any observer outside of the water.
What we see and how different it can
be from what it seems to be
• The woman will see the
underwater part of body being
a) Smaller than it really is;
b) Much larger than it really is;
c) Of natural size;
What we see and how different it can
be from what it seems to be
• The woman will see the
underwater part of body being
a) Smaller than it really is;
b) Much larger than it really is;
c) Of natural size;
What we see and how different it can
be from what it seems to be
• The boy will see the underwater
part of body being
a) Smaller than it really is;
b) Much larger than it really is;
c) Of natural size;
Total internal reflection is an extreme case of a ray bending away
from the normal as it goes from a higher to a lower index of
refraction medium (from a slower to a faster medium)
Just below the critical angle fo
internal reflection there is a ref
and a transmitted (refracted) ra
Normal
Air (fast medium)
Glass or
water
Critical(slow)
angle
Just above the critical angle fo
internal reflection there is a ref
but no transmitted (refracted) r
Normal
For the glass-air
interface
Glass or
water
(slow)
Total internal reflection
• Show that the internal
reflection is a
consequence of the
Snell’s law
• The precise amount of
bending is determined by the
law of refraction (sometimes
called Snell's law):
•
ni sinqi = nt sinqt
• Here, qi = angle between
incident ray and normal,
• and qt = angle between
transmitted ray and normal
• ni and nt are the indices of
refraction in the medium
containing the incident ray and
in the medium containing the
transmitted ray
What we see and how different it can
be from what it seems to be
• If the critical angle condition
is satisfied, will the boy see
the part of body above water:
a) yes;
b) No.
• Extra Credit:
Refractive index of water is 1.33;
What is the critical angle for
the case of air-water interface?