Download Sunday, September 14, 2003 غامر الحكيم 057403435 حمود العويد

Sunday, September 14, 2003
004705750 ‫غامر الحكيم‬
005887550 ‫حمود العويد‬
Ch 1: Nature of light
What is light?
Is light a particle or a wave?
Isaac Newton – English - 1643-1727: light is a particle
Because it casts sharp shadows.
Failed to explain the Newton’s rings correctly
Christian Huygens –Dutch- 1629 - 1695: light is a wave motion.
When two light beams intersect, they emerge unmodified.
Light is a longitudinal wave travels in ether
Thomas Young - English - 1773-1829. Double-slit experiment
Decisive experiment support the wave theory of light
Augustin Fresnel – French - 1788-1827. Light is a transverse wave
In 1821, from experiment and analysis light is a transverse wave. Liquid
(ether) can not support transverse wave – problem..
James Clerk Maxwell- Scottish 1831-1879. Light is an electromagnetic wave
His equations predict that electromagnetic wave has the same speed as of
light. Light is an electromagnetic wave
Albert Michelson-German-American - 1852-1931. no ether
In 1887, Not able to detect the earth’s motion through the ether.
Albert Einstein German-American - 1879-1955. No ether
In 1905, Theory of relativity
Max Plank German- 1858-1947 atom emits light in discrete energy - photons
In 1900, he was able to derive the correct blackbody spectrum by assuming
that atoms emit light in discrete energy chunks
E=h
Albert Einstein – light is a stream of photons
In 1905, explain photo electric effect based on Planck’s photon idea.
Neil Bohr- Danish - 1885-1962- light consists of photons
In1913, explained emission and absorption processes of the hydrogen atom by
using photon model of light
Arthur Compton – American - 1892-1962. photon model of light
In 1922, explained the scattering of x-ray from electron using the photon
model of light.
Luis de Broglie – French - 1892-1987 – duality principle
In 1924, All particle have wave-like property with a wave length given by
=h/p.
Photons and electron behave like particles and waves. The are neither waves
nor particles.
Clinton Davisson –American- 1881-1958. Confirmed de Broglie theory.
Lester Germer – American - 1896-1971 Confirmed de Broglie theory
In 1925, Both Davisson and Germer observed diffraction of electrons
Sir George Thomson – English - 1892-1975 Confirmed de Broglie theory
In 1927, he observed diffraction of electrons.
1
 
1

v
1  ( )2
c
Rest mass
Relativistic mass
Rest energy
Total energy
momentum
general
photon
m
m
0
mc 2
0
E  pc
E  ( pc) 2  (mc 2 ) 2
E  rest enerngy  kinetic energy
h
p  mv 

speed
v  c 1
(mc 2 ) 2
E2
p
h

c
Example
The wave description of light will be adequate for most of the optical phenomenal in
this book.
2
Sunday, September 14, 2003
Ch 3: Geometrical Optics
1- Huygens’ principle
2- Fermat’s principle
3- Principle of reversibility
4- Reflection in plane mirrors
5- Reraction through plane surfaces
6- Imaging by an optical system
7- Reflection at a spherical surface
8- Refraction at a spherical surface
9- Thin lenses
10- Vergence and refractive power
11- Newtonian equation for thin lens
3-0- Introduction
Have you ever observed waves on the surface of water hitting an obstacle? The
waves bend around obstacles. This is why you can hear sound although you are not
sitting directly on the path of the sound source around the corner. This bending is
called diffraction. But why can you not easily observe this for light. Light casts sharp
shadows.
The amount of bending depends on the size of the wavelength compared to the
opening. Typically for sound wave of 1 kHz frequency, the wavelength is roughly 34
cm, while for light it is typically of order of 0.5 m, about 1/100 of your hair
diameter. This why, long time ago, people like Newton, thought light was not a wave.
They were not able to observe its diffraction; the used large apertures.
3
If we are not dealing with small openings compared to the size of the wavelengths of
light, we may ignore diffraction and represent light as rays moving in straight lines.
These rays are paths along which energy is transmitted from one point to another.
These rays are abstract useful in studying light; they are not real.
The branch of optics in which we ignore diffraction and represent light as rays
moving in straight lines is called geometrical optics. In this branch of optics,
Geometrical relationships are used to study light.
The branch of optics in which we consider diffraction, is called physical optics. In
effect, Geometrical optics is physical optics in which wavelength of light is set to
zero.
phyisical Optics  Geometical Optics
 0
A ray of light moves in a straight line if it travels in a homogenous medium and
changes its direction at the boundary between homogenous media. This change in
direction is governed by two laws: law of reflection and law of refraction.
Law of reflection: A ray of light is reflected at the interface of two uniform medium
such that
 The reflected ray remains in the plane of incidence.
 The angle of reflection equals to angle of incidence.
Law if refraction: A ray of light is refracted at the interface of two uniform medium
such that
 The refracted ray remains in the plane of incidence.
 The sine of angle of refraction is proportional to the sine of angle of incidence.
Plane of incidence includes the incident ray and the normal of the interface at the
point of incidence.
We will use Huygens’ principle and Fermat’s principle to derive these laws.
Figure
3-1- Huygens’ Principle
Each point in the leading surface of a wave disturbance –the wave front- may be
regarded as a secondary source of spherical waves (wavelet) which themselves
progress with speed of light in the medium and whose envelope at a later time
constitutes the new wave front.
 The envelope is tangent to the wavelet just at one point, the rest is ignored.
 The wave front formed by the back half of the wavelets is also ignored.
# Plane front
# Spherical front
# obstructed wave front
Weakness of the model is remedied by Fresnel and others.
4
# Derivation law of reflection
normal triangle
# Derivation of law of refraction
3-2- Fermat’s Principle
The actual path taken by a ray of light in its propagation between two points is the
path of the shortest time.
# Derivation law of reflection
# Derivation of law of refraction
3-3- Principle of reversibility
Any actual ray of light in an optical system, if reverse in direction, will trace the same
path backward.
3-4- reflection in plane mirrors
specular reflection; reflection from perfectly smooth surface
diffuse reflection: reflection from rough surface.
Reflection from a mirror in xy-plane
(x, y, z)  (x, y, -z)
Reflection from three mirrors one in xy-plane, one in yz-plane and one in zx-plnae
(x, y, z) (-x, -y, -z)
Reflected ray parallel to the incident ray.
Image from a point
 lies along the normal
 The image distance is equal to the object distance
 Virtual image:
o The eye sees it as if a real object is placed there but no ray originates
from it and
o it can not projected on a screen.
 Mirror can be extended to find out the position of the mirror
 Its position does not depend on the eye position
Image from extended object
 image size = object size
magnification of unity
 transverse orientation is the same
 left-handed appears right-handed
Images of a point of two perpendicular mirrors
3-5- refraction through plane surfaces
5
# when light bends toward or away from the normal.
# Incident normal to the surface zero is transmitted without change in direction
# Three refracted light rays; no unique image point by refracted rays; they do not
intersect at the same point.
## Why do see relatively good image under water?
n
- for small incident angle – paraxial approximation  s   1 s
n2
1
3
s s
o for water-air interface s  
1.33
4
- for large incident angles; your eye aperture – pupil – accepts only a small
bundle of rays and they appear to originates form the same point.
3
o s  s
4
- total internal reflection
n
o critical angle sin  c  2
n1
o occurs only for n1  n2
Sunday, September 21, 2003
3-6 Imaging by an optical system
Figure 3-10
Object space
Optical system
Image space
Wave front and transit time
Isochronous
I  O
conjugate points
Ideal Optical system
Every ray from the object point intercepted by the system and only these raysalso passes thorough the image point.
In practice there is no ideal system because; no ideal image
1- light scattering
 reflection losses
 scattering by in homogeneities
2- aberration
 no one-to-one relationship between object and image
3- diffraction
 diffraction-limited
Cartesian surfaces reflecting or refraction forms perfect images
Reflection  conic surfaces
 ellipsoid
 hyperboloid
6

paraboloid
image at infinity
Refraction  Ovoid of revolution ‫بيضي الشكل‬
 same optical medium
o Double hyperbolic lens
 Spherical lens is much easier to fabricate
3-7 Reflection at a spherical surface
1 1
2
 
s s
R
Gaussian optics = first order optics = paraxial optics
The exterior angle of a triangle equals the sum of its interior angles.
# Derivation of


# Sign convention
 real object and image  positive object and image
 R > 0 for convex mirror
# 
2 1

R f
object @ infinity  image at focal point
# Derivation of lateral (transverse) magnification m  
s
s
# Graphical construction
# Example 46
3-8 Refraction at a spherical surface
# Derivation of
n1 n2 n2  n1


s s
R
m
n1 s 
n2 s
# Example 49
# If a number of surfaces is involved, they are considered in the order in which light is
actually incident on them. The object distance of the jth step is determined from the
image distance of the (j-1)th step. If the image of the (j-1)th step is not formed, it
serves as a virtual image of the jth step.
3-9 Thin lenses
# Derivation of
#
1 1 n2  n1 1
1
 
(  )
s s
n1
R1 R2
1 n2  n1 1
1

(  )
f
n1
R1 R2
# Magnification
7
# magnification
m
s
s
# Sample rays
 Parallel

 Through focus
 Through center
Through focus

Parallel

Straight
# Example p. 54
3-10 Vergence and refractive power
1 1 1
 
s s f
Vergence
1/f
V V  P
curvature
refractive power
unit diopter
D
3-11 Newtonian Equation for the thin lens
# derivation
xx   f
2
8
Tuesday, September 30, 2003
Ch 4: Matrix Methods in Paraxial Optics
Simplifying study of optical system
4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
4-9
4-10
4-11
The thick lens
The matrix method
The translation matrix
The refraction method
The reflection method
Thick-lens and thin-lens matrix
System ray-transfer matrix
Significance of system matrix elements
Location of cardinal points for an optical system
Example using the system matrix and cardinal points
Ray tracing
4-1- The thick lens
we can use the method in the last chapter to study image formation from thick lens.
We will consider another method using cardinal points ‫رئيسي‬.
There are six cardinal points on the axis.
1- fist focal point
F1
2- second focal point
F2
3- first principal point
H1
4- second principal point
H2
5- first nodal point
N1
6- second nodal point
N2
# Cardinal planes
# Definition of cardinal points of an optical system
# Distance sign convention
to the right = positive
For object and image we will have our old convention.
Object: left to H1 positive
Image Left to H2 negative and right to H2 positve
# Definition of distances
# Equations of cardinal points for thick lens without proof
# Example
4-2 The matrix method
The matrix method describes the change in height and angle of a ray as it makes its
way by successive refraction and reflections through the optical system.
We can describe the effect of the hole system by one matrix.
4-3 The translation matrix
# Derivation
9
4-4 The refraction method
# Derivation
4-5 The reflection method
# Derivation
# Sign convention for the
angles
R
pointing upward = positive
convex = positive
4-6 Thick-lens and thin-lens matrix
# Matrix order
multiplication is not commutative
4-7 System ray-transfer matrix
# ABCD matrix
# Values depend on the position of input and output plane
DetM 
n0
n1
Tuesday, September 30, 2003
HW#3
3-12, 3-16, 3-18, 3-19, 3-22
4-8 Significance of system matrix elements
# derivation
# example
4-8 Location of cardinal points for an optical system
# derivation
4-10
Example using the system matrix and cardinal points
Tuesday, October 07, 2003
Ch 6: Optical instumentation
6-1
6-2
6-3
6-4
6-5
6-6
6-1
Stops, pupil, and windows
Prisms
The camera
Simple magnifier and eyepieces
Microscopes
Telescope
Stops, pupil, and windows
Image brightness: aperture stops and pupils
Aperture stops (AS)
10

actual optical system that limits the size of the maximum cone rays
from an axial object point that can be process by the optical system
 It controls the brightness of the image
 Need not to be the first object. Example 6-1a
Entrance Pupil (EnP)
 The image of the aperture stop formed by the optical elements that
proceeds it
 The limiting aperture that the ray sees looking into optical system from
the object.
 Can be virtual. . Example 6-1b
Exit Pupil (ExP)
 The image of the aperture stop formed by the optical elements that
follows it
 The limiting aperture that the ray sees looking into optical system from
the image
# ExP, and EnP are conjugate: rays intersecting the edges of the entrance pupil also
intersect the edges of the exit pupil; and aperture stop.
Chief (principal) Ray: is a ray from object point that passes through the axial point in
the plane of the entrance pupil  through exit pupil and aperture stop
# example : which optical element that has an entrance pupil that confines rays to
their smallest angle with the axis as seen from the object point.
Field of View: Field stops and Windows
Window on the wall
Fig 6-3
Vignetting
Lateral field of view
Field of view
Field stop (FS) : the real aperture that limits the angular field of view formed by an
optical system.
 limiting the solid angle formed by chief rays.
 As seem by the entrance pupil, FS or its image subtended the smallest
solid angle.
 To sharply delineate FS, put it in the image plane
 Used to reduce aberration and vignetting
Entrance Window (EnW)
Exit Window (ExW)
Example: relation between field view and entrance and exit pupil
11
6-2
Prisms
Angular deviation of a Prism
Minimum deviation
Deviation of a prism with a small apex angle
Dispersion = refractive index is a function of the wavelength
Normal and anomalous dispersion
Cauchy formula
Dispersion =dn/d
Dispersion and deviation
Fraunhofer lines
Dispersive power
Prism Spectrometer
Chromatic resolving power
n  nD

dn
R
b
b F

d
F  D
Field of view: field stops and windows
Quadrilateral ‫رباعي االضالع‬
Sunday, November 30, 2003
Ch 11: Optical Interferometry
Wavefront-division interferometer
Amplitude-division interferometer
Young’s double slits
Michelson interferometer
Two beam
Multiple beams
Michelson interferometer
Fabry Perot
11-1
The Michelson Interferometer
12