exam 1 is finished, avg: 84 +/- 10.5 solutions on the web ... of specular reflection of a ray from a...
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1
Physics 1230: Light and Color
Lecture 6:
Reflection, mirror images, and refraction.
Reading: Chapter 2, pgs. 29-68
Exam 1 is finished, Avg: 84 +/- 10.5
Solutions on the web and scores on CULearn.
HW4: Due Thursday, 5PM
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Chapter 2 – Geometrical Optics
1. Shadows
2. Reflection
3. Refraction
4. Dispersion
We
are
here
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
3
Chapter 2 – Geometrical Optics
1. Shadows
2. Reflectiona) Specular or diffuse
b) Equal angle rule
c) Mirror images, ray tracing
3. Refraction
4. Dispersion
a. Point source or diffuse source
b. Umbra and penumbra
c. How tall is my shadow?
d. Pinhole camera
We
are
here
Specular or diffuse?
Diffuse reflection
(paper)
Specular reflection
(mirror)
Diffuse transmission
(wax paper)
4
Equal angle rule
5
qrqi
Normal
Mirror
qi = angle of incidence
qr = angle of reflection
qi = qr is specular reflection
A normal is a line
perpendicular to
the surface.
Incident RayReflected Ray
Plasma frequency of silver
Materials like metals with many mobile electrons can cancel
out the light wave field in the forward direction so there is no
transmission but only reflection at certain wavelengths.
• Metals reflect all waves below a
certain frequency
– the plasma frequency - which
varies from metal to metal
• Silver is particularly interesting
because it reflects light waves at all
visible frequencies
– Its plasma frequency is at the top
of the violet so it reflects all of the
wavelengths below and appears
whitish
• Gold and copper have a yellowish-
brownish color because they reflect
greens, yellows and reds but not
blues or violets
– Red and green make yellow
Plasma frequency of gold
Plasma frequency of copper
What is a mirror?
• Since silver is such a good
reflector a coating of silver on
glass makes 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
Mirror
This angle = this angle
The normal to the mirror is an imaginary
line drawn perpendicular to it from where
the incident ray hits the mirror
Normal
• One of many rays from a light bulb
hits Alex's chin.
• The ray from the light bulb is
diffusely reflected off his chin. We
show one of the many rays coming
off his chin hitting a mirror.
– This is called an incident ray
• The incident ray undergoes
specular reflection off the mirror
– Note the reflected ray
• Draw the normal to the mirror
– The angle of incidence = the angle
of reflection
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
– Consider an incident ray from Alex's chin
which reflects according to the law of
reflection at a specific point on the mirror
and goes into Bob's eye.
– Note - it is not easy to construct this ray!
You cannot arbitrarly choose a point on the
mirror and expect that the law of reflection
will be satisfied
– Bob will see only this reflected ray from
Alex's chin.
– Other refelected rays from Alex's chin will
miss his eye (see right)
– A ray from Alex's hair will reflect at one
point on the mirror into Bob's eye (and
satisfies the law of reflection)
Mirror
AlexBob looks at
Alex's image
• To find the image of Alex we must learn how Bob’s eye (and our eyes) interpret rays
• Bob cannot directly know whether the rays entering his eyes have been reflected or not!
• We interpret all rays coming into our eye as traveling from a fictitious imagein a straight line to our eye even if they are reflected rays!
• To find the virtual (fictitious) image of Alex’s chin we extend each reflected ray backwards in a straight line to where there are no real rays
– Extend the ray reflected into Bob's eye from Alex's chin backward behind the mirror.
– Extend the ray reflected towards Bob's chest (why?) from Alex's chin backward (dashed line) behind the mirror.
– The image of Alex's chin will be behind the mirror at the intersection of the two backward-extended reflected rays.
– Note all reflected rays from his chin intersect at
the same image pt. when extended backwards
How is an image produced in a mirror?
Part 2: The psychology of ray interpretation
Mirror
Alex Bob looks at
Alex's image
• To find the location of his hair in the virtual image we extend any reflected ray from his hair backwards
How is an image produced in a mirror?
Part 3: 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. It is virtual because
there is no light energy there, no real rays
reach it, and it cannot be seen by putting
a screen at its position!!
Virtual image of Alex
is behind mirror
Mirror
Alex
• When all of the reflected rays from Alex's
chin are traced backwards they all appear to
come from the virtual image of Alex’s chin
– Hence Alex's image is always in the
same place regardless of where Bob looks
• The image chin is behind the mirror by a
distance = to the distance the real chin is in
front of the mirror
– This is true for all parts of Alex's image
– Alex's virtual image is the same size as
the real Alex
– Alex's image is further away from Bob
than the real Alex
Bob looks at
Alex's image
Bob sees Alex's image
in the same place when
he moves his head
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.
12Xobject Ximage
normal
extended
Mirror
Ray tracing: Draw the image, then the rays
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Xobject Ximage
Mirror
First: draw rays from image to eyes
Viewed from the side.
Ray tracing: Draw the image, then the rays
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Xobject Ximage
Mirror
First: draw rays from image to eyes
Second: draw rays from mirror to object
qi = qr happens automatically using this method. Demo on board
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Xobject Ximage
Mirror
The top ray goes to the top of the bottle.
It is right side up.
qi = qr happens automatically using this method.
Right side up image?
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Xobject
Ximage
Mirror(to do this drawing,
the mirror must be extended)
The top ray goes to the bottom of the bottle.
It is upside down.
qi = qr happens automatically using this method.
Right side up image?
Extension
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Mirror(to do this drawing,
the mirror must be extended)
qi = qr happens automatically using this method.
Bottle on its side
Viewed from the side.
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
A few words about virtual images
• Here is the real Alex
• Here are some (diffusely reflected) diverging rays coming off his nose
– They can be seen by eyes at various locations
• We only know his nose is there because our eyes receive the rays
• Therefore, we would see an image (virtual) of Alex if those rays reached our eyes even when he wasn't there.
• Mirrors can provide those rays!
• The (imaginary) extension of (reflected) rays behind the mirror look just like the real rays from the real Alex
Mirror (incident
rays not shown)
Periscope
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mirror
mirror
The image of the
bottle in the lower
mirror is:
A) Inverted
B) Not inverted
C) Something else
Original
OBJECT
Periscope?
21
extension
Original
OBJECT
The first IMAGE
Periscope?
22
extension
The second IMAGE
Periscope?
23
The image of the
bottle in the lower
mirror is:
A) Inverted
B) Not inverted
C) Something else
Mirror
Alex• Question: Where are
the images of Alex in the 2 mirrors?
a) At A only
b) At B only
c) At A and B only
d) At C only
e) At A, B and C
Multiple mirrors - a virtual image can act as a
real object and have its own virtual image
Mirror
A C
B
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.
25
Is the writing reversed?
AR
(Two mirrors, viewed from above)
A) YES
B) NO
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Is the writing reversed?
AR
ЯA
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Is the writing reversed?
AR
ЯA
AR
extension
28
Is the writing reversed?
AR
ЯA
AR
A) YES
B) NO
2929
Lec. 6: Ch. 2 - Geometrical Optics
1. Shadows
2. Reflection
3. Refraction
4. Dispersion
We
are
here
30
Refraction
1. Index of refraction: n = c / v
2. Ray in water is closer to the normal
3. Total internal reflection
4. Mirages
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
– 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).
• When light waves are incident
on a glass slab they are mostly
transmitted but partly reflected
(about 4%)!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
(EM) wave is constant (for every
wavelength) in empty space!
• The speed of light is slower than c
in glass, water and other
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 is reflected and
transmitted at a boundary
because
– When a light wave travels in a
medium the electric field of the
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
Material Refractive Index
Air 1.0008
Water 1.330
Glass 1.5
Diamond 2.417
Ruby 1.760
Oil 1.5
Refractive indices of different materials
Can we see a glass rod immersed
into the oil with the same
refractive index?
• A. Yes
• B. No
Demo