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
Newton
• Used this particle model to explain reflection
and refraction
Huygens
• 1670
• Explained many properties of light by
proposing light was wave-like
A Brief History of Light, cont
Young
• 1801
• Strong support for wave theory by
showing interference
Maxwell
• 1865
• Electromagnetic waves travel at the
speed of light
A Brief History of Light, final
Planck
• EM radiation is quantized
Implies particles
• Explained light spectrum emitted by hot
objects
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?
Detection of light directly emitted by
object
Detection of light reflected by object
(most common)
Ray Optics – Using a Ray
Approximation
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
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
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
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
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
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
The normal is a line
perpendicular to the
surface
• It is at the point where
the incident ray strikes
the surface
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
The angle of reflection is equal to the
angle of incidence
θ1= θ1’
Reflection and Mirrors
q1
q1 = q1
q1
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
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
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
q1
n > 1
q2
n1sinq1 = n2sinq2
q1
q1
q2
water
q1> q2
Total Internal Reflection
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
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
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
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
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
These are
examples of
converging lenses
They have positive
focal lengths
They are thickest
in the middle
More Thin Lens Shapes
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
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
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
One can show
25
mq
(standard)
f
25
mq
1 (maximum)
f
f must be in cm
Example
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
View Distant Objects
(Angular) Magnification M=fobj/feye
Increased Light Collection
Large Telescopes use Mirrors