Transcript 11-29

Chapter 22, 23
Ray Optics, Mirrors, Lenses, Image
and Optical Instruments
A Brief History of Light

1000 AD
• It was proposed that light consisted of tiny
particles
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Newton
• Used this particle model to explain reflection
and refraction
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Huygens
• 1670
• Explained many properties of light by
proposing light was wave-like
A Brief History of Light, cont
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Young
• 1801
• Strong support for wave theory by
showing interference
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Maxwell
• 1865
• Electromagnetic waves travel at the
speed of light
A Brief History of Light, final
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Planck
• EM radiation is quantized
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Implies particles
• Explained light spectrum emitted by hot
objects
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Einstein
• Particle nature of light
• Explained the photoelectric effect
C = fl
C: speed of light
C = 3 x 108 m/s
in vacuum
EM wave can travel
in the absence of medium.
In other medium, the
speed of light is
smaller than in vacuum.
3 x 108 = f l
nano = 10-9
http://laxmi.nuc.ucla.edu:8248/M248_99/iphysics/spectrum.gif
How do we see an object?
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Detection of light directly emitted by
object
Detection of light reflected by object
(most common)
Ray Optics – Using a Ray
Approximation
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Light travels in a straight-line path
in a homogeneous medium until it
encounters a boundary between
two different media
The ray approximation is used to
represent beams of light
A ray of light is an imaginary line
drawn along the direction of travel
of the light beams
The Index of Refraction
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Speed of light c= 3x 108 m/s in
vacuum.
Speed of light is different (smaller) in
other media
The index of refraction, n, of a
medium can be defined
speed of light in a vacuum c
n

speed of light in a medium v
Index of Refraction, cont
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For a vacuum, n = 1
For other media, n > 1
n is a unitless ratio
Normal air: 1.0003
Water: 1.33
Flint glass: 1.66
Diamond 2.42
Reflection of Light
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A ray of light, the incident ray,
travels in a medium
When it encounters a boundary with
a second medium, part of the
incident ray is reflected back into the
first medium
• This means it is directed backward into
the first medium
Specular Reflection
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Specular reflection
is reflection from a
smooth surface
The reflected rays
are parallel to each
other
All reflection in this
text is assumed to
be specular
Diffuse Reflection
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Diffuse reflection is
reflection from a
rough surface
The reflected rays
travel in a variety
of directions
Diffuse reflection
makes the road
easy to see at
night
Law of Reflection
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The normal is a line
perpendicular to the
surface
• It is at the point where
the incident ray strikes
the surface
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The incident ray
makes an angle of θ1
with the normal
The reflected ray
makes an angle of θ1’
with the normal
Law of Reflection, cont
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The angle of reflection is equal to the
angle of incidence
θ1= θ1’
Reflection and Mirrors
q1
q1 = q1
q1
Law of reflection
Specular Reflection
Diffuse Reflection
When we talk about an image, start from an ideal point light source.
Every object can be constructed as a collection of point light sources.
VIRTUAL
IMAGE
p
|q|
Image forms at the point where the light rays converge.
When real light rays converge  Real Image
When imaginary extension of L.R. converge  Virtual Image
Only real image can be viewed on screen placed at the spot.
VIRTUAL
IMAGE
p
|q|
For plane mirror: p = |q|
How about left-right?
p: object distance
q: image distance
Let’s check?
Spherical Mirror
R: radius of curvature
focal Point
f: focal length = R/2
Optical axis
concave
convex
Parallel light rays: your point light source is very far away.
Focal point:
(i) Parallel incident rays converge after reflection
(ii) image of a far away point light source forms
(iii) On the optical axis
Reflected rays do not converge:
Not well-defined focal point
 not clear image
Spherical Aberration
f = R/2 holds strictly for a very
narrow beam.
Parabolic mirror can fix this problem.
Case 1: p > R
p
f
P>q
Real Image
q
Case 2: p = R
p=q
Real Image
Case 3: f < p < R
p<q
Real Image
Case 4: p = f
q = infinite
Case 5: p < f
q<0
Virtual Image
Mirror Equation
1/p + 1/q = 1/f
For a small object, f = R/2 (spherical mirror)
1/p + 1/q = 2/R
Alert!!
Be careful with the sign!!
Negative means that it is inside the mirror!!
p can never be negative (why?)
negative q means the image is formed inside the mirror
VIRTUAL
How about f?
For a concave mirror: f > 0
Focal point inside the mirror
f < 0
1/p + 1/q = 1/f < 0 : q should be negative.
1/p + 1/q = 1/f < 0 : q should be negative.
All images formed by a convex mirror are VIRTUAL.
Magnification, M = -q/p
Negative M means that the image is upside-down.
For real images, q > 0 and M < 0 (upside-down).
Example: An object is 25 cm in front of a concave spherical
mirror of radius 80 cm. Determine the position and
characteristics of the image.
1/p + 1/q = 1/f
f = R/2 = 40 cm
Object is at the center: p = 25 cm
1/q = 1/40 – 1/25
= -0.015
q = -66.7 cm < 0 (Virtual Image, 66.7 cm behind mirror)
M = -q/p = -(-66.7)/25 = 2.7
Erect, 2.7 times the size of the object
Example: What kind of spherical mirror must be used, and
what must be its radius, in order to give an erect image 1/5 as
Large as an object placed 15 cm in front of it?
M = -q/p  -q/p=1/5
So q = -p/5 = -15/5 = -3 cm
1/p + 1/q = 1/f  1/15 - 1/3 = 1/f
1/f = (1-5)/15
f = -15/4 = -3.75 cm
R = 2 f = -7.5 cm Convex
Example: Where should an object be placed with reference to
a concave spherical mirror of radius 180 cm in order to form a
Real image having half its size?
M = -q/p  -q/p=-1/2
So q = p/2
f = R/2 = 90 cm
1/p + 1/q = 1/f  1/p + 2/p = 1/f
3/p=1/90
p = 270 cm
Refraction Details, 1
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Light may refract
into a material
where its speed is
lower
The angle of
refraction is less
than the angle of
incidence
• The ray bends
toward the normal
Refraction Details, 2
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Light may refract
into a material
where its speed is
higher
The angle of
refraction is
greater than the
angle of incidence
• The ray bends away
from the normal
Snell’s Law
All three beams (incident, reflected, and refracted) are in one plane.
q1
q1
n > 1
q2
n1sinq1 = n2sinq2
q1
q1
q2
water
q1> q2
Total Internal Reflection
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Total internal
reflection can occur
when light
attempts to move
from a medium
with a high index
of refraction to one
with a lower index
of refraction
• Ray 5 shows
internal reflection
Critical Angle
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A particular angle
of incidence will
result in an angle
of refraction of 90°
• This angle of
incidence is called
the critical angle
n2
sin q 
for n1  n2
n1
Critical Angle, cont
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For angles of incidence greater than the
critical angle, the beam is entirely
reflected at the boundary
• This ray obeys the Law of Reflection at the
boundary
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Total internal reflection occurs only when
light attempts to move from a medium of
higher index of refraction to a medium of
lower index of refraction
Examples of critical angles (relative to vacuum)
Substance
N
Critical angle
1
90.0
Air
1.00029
88.6
Ice
1.31
49.8
Water
1.333
48.6
Ethyl Alcohol
1.36
47.3
Glycerine
1.473
42.8
Crown glass
1.52
41.1
Sodium chloride
1.54
40.5
Quartz
1.544
40.4
Heavy flint glass
1.65
37.3
Tooth enamel
1.655
37.2
Sapphire
1.77
34.4
Heaviest flint glass
1.89
31.9
Diamond
2.42
24.4
Vacuum
sin q crit
1

n
How could fish survive from spear fishing?
Fish vision
qf = 2qc
qc = sin-1(1/1.33)
= 49
> ncore nclad
Lenses
Converging lens
Diverging lens
Thin Lenses
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A thin lens consists of a piece of
glass or plastic, ground so that each
of its two refracting surfaces is a
segment of either a sphere or a
plane
Lenses are commonly used to form
images by refraction in optical
instruments
Thin Lens Shapes
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These are
examples of
converging lenses
They have positive
focal lengths
They are thickest
in the middle
More Thin Lens Shapes
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These are
examples of
diverging lenses
They have
negative focal
lengths
They are thickest
at the edges
Glass lens (nG = 1.52)
The focal length of a lens is determined by the shape
and material of the lens.
Same shape lenses: the higher n, the shorter f
Lenses with same n: the shorter radius of curvature,
the shorter f
Typical glass, n = 1.52
Polycarbonate, n = 1.59 (high index lens)
Higher density plastic, n ≈ 1.7 (ultra-high index lens)
Rules for Images
• Trace principle rays considering one end of an object
•
•
•
•
off the optical axis as a point light source.
A ray passing through the focal point runs parallel to
the optical axis after a lens.
A ray coming through a lens in parallel to the optical
axis passes through the focal point.
A ray running on the optical axis remains on the optical
axis.
A ray that pass through the geometrical center of
a lens will not be bent.
Find a point where the principle rays or their imaginary
extensions converge. That’s where the image of the point source.
two focal points: f1 and f2
Parallel rays: image at infinite
Virtual image
Magnifying glass
Virtual image
Lens equation and magnification
1/p + 1/q = 1/f
M = -q/p
This eq. is exactly the same as the mirror eq.
Now let’s think about the sign.
positive
negative
p
real object
virtual object
(multiple lenses)
q
real image
(opposite side of object)
virtual image
(same side of object)
f
M
for converging lens
for diverging lens
erect image
inverted image
1/p + 1/q = 1/f
1/2f + 1/q = 1/f
1/q = 1/2f
M = -q/p = -1
two focal points: f1 and f2
1/p + 1/q = 1/f
1/f + 1/q = 1/f
1/q = 0  q = infinite
Parallel beams: image at infinit
Virtual image
Magnifying glass
1/p + 1/q = 1/f
2/f + 1/q = 1/f
1/q = -1/f
M = -(-f)/(f/2) = 2
Virtual image
positive f
Example: A thin converging lens has a focal length of 20 cm.
An object is placed 30 cm from the lens. Find the image
Distance, the character of image, and magnification.
f = 20, p = 30
1/q = 1/f – 1/p
= 1/20 – 1/30
= 1/60
q = 60
real image (opposite side)
M = -q/p
= -60/30
= -2 < 0 inverted
Magnifier
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Consider small object held in front of eye
• Height y
• Makes an angle q at given distance from the
eye
Goal is to make object “appear bigger”: q' > q
y
q
Magnifier
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Single converging lens
• Simple analysis: put eye right behind lens
• Put object at focal point and image at infinity
• Angular size of object is q, bigger!
Outgoing
rays
Rays seen coming
from here
q
f
y
q
f
Image at
Infinity
1 1 1
 
q f p
(angular) Magnification
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One can show
25
mq 
(standard)
f
25
mq 
 1 (maximum)
f
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f must be in cm
Example
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Find angular magnification of lens
with f = 5 cm
25
mq 
5
5
25
mq 
1  6
5
Standard
Maximum
Combination of Thin Lenses,
example
Telescope
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View Distant Objects
(Angular) Magnification M=fobj/feye
Increased Light Collection
Large Telescopes use Mirrors