Polarization and it's application in OphthalmologyRaju Kaiti
Polarization, types of polarization, mechanisms to produce polarization, Applications of polarization, precautions with polarizing sunglasses, ophthalmic uses of polarization
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
Polarization and it's application in OphthalmologyRaju Kaiti
Polarization, types of polarization, mechanisms to produce polarization, Applications of polarization, precautions with polarizing sunglasses, ophthalmic uses of polarization
What is Polarization?
Types of polarized light
Few related terms
Few laws related to polarization
Applications
FOR MORE VISIT: https://tariqalfayad.blogspot.com/
Laser is very important technological device these days.There is a use of laser in almost every field of science and technology. It also gives it's application in medicines also.
This presentation shows how it works and what is the mechanism behind this laser phenomenon. Here it is explained from atom theory to application.
Very good explanation with photographs.
A detailed presentation on fraunhofer diffraction and also an introduction to the concept of diffraction.There is also a brief discussion on fresnel diffraction and the difference between former and the latter.
Laser is very important technological device these days.There is a use of laser in almost every field of science and technology. It also gives it's application in medicines also.
This presentation shows how it works and what is the mechanism behind this laser phenomenon. Here it is explained from atom theory to application.
Very good explanation with photographs.
A detailed presentation on fraunhofer diffraction and also an introduction to the concept of diffraction.There is also a brief discussion on fresnel diffraction and the difference between former and the latter.
Lens history and physics.
For comments please contact me on solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics folder.
[Electricity and Magnetism] ElectrodynamicsManmohan Dash
We discussed extensively the electromagnetism course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around 9th November 2009. I added all the diagrams and many explanations only now; 21-23 Aug 2015.
Next; Lectures on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org
Optical Aberration is the phenomenon of Image Distortion due to Optics Imperfection.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics Folder. Since some of the Figures were not downloaded I recommend to see the presentation on my website.
Gravitational lensing for interstellar power transmissionSérgio Sacani
We investigate light propagation in the gravitational field of multiple gravitational lenses. Assuming these lenses are sufficiently spaced to prevent interaction, we consider a linear alignment for the
transmitter, lenses, and receiver. Remarkably, in this axially-symmetric configuration, we can solve
the relevant diffraction integrals – result that offers valuable analytical insights. We show that the
point-spread function (PSF) is affected by the number of lenses in the system. Even a single lens is
useful for transmission either it is used as a part of the transmitter or it acts on the receiver’s side.
We show that power transmission via a pair of lenses benefits from light amplification on both ends
of the link. The second lens plays an important role by focusing the signal to a much tighter spot;
but in practical lensing scenarios, that lens changes the structure of the PSF on scales much smaller
than the telescope, so that additional gain due to the presence of the second lens is independent of its
properties and is govern solely by the transmission geometry. While evaluating the signal-to-noise
ratio (SNR) in various transmitting scenarios, we see that a single-lens transmission performs on par
with a pair of lenses. The fact that the second lens amplifies the brightness of the first one, creates a
challenging background for signal reception. Nevertheless, in all the cases considered here, we have
found practically-relevant SNR values. As a result, we were able to demonstrate the feasibility of
establishing interstellar power transmission links relying on gravitational lensing – a finding with
profound implications for applications targeting interstellar power transmission.
Method for measuring or investigation of fiber structureShawan Roy
Method for measuring or investigation of fiber structure (details about optical and X-ray diffraction & electron microscopy and electron diffraction method)
Engineering Physics, Interference of Light, Michelsons Interferromter, Newtons Ring, Diffraction, Diffraction from Single Slit, Diffraction from grating, Resolving Power
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
1. Ray Optics
Light is an electromagnetic wave phenomenon described by
the same principles that govern all forms of electromagnetic
radiation. Electromagnetic radiation propagates in the form of
two mutually coupled vector waves, an electric – field wave and
a magnetic – field wave. Nevertheless, it is possible to describe many optical
phenomena using a scalar wave theory in which light is described by a single
scalar wave function. This approximate way of treating light is called wave op-
tics, or simply wave optics.
In free space, light waves travel with a constant speed .
The range of optical wavelengths contains three bands – ultraviolet (10 to 390
nm), visible (390 to 760 nm), and infrared (760 nm to 1 mm). The corres-
ponding range of optical frequencies stretches from
.
When light waves propagate through and around objects whose dimensions
are much greater than the wavelength, the wave nature of light is not readily
discerned, so that its behavior can be adequately described by rays obeying a
set of geometrical rules. This model of light is called ray optics. Strictly speak-
ing, ray optics is the limit of optics when the wavelength is infinitesimally
short. However, the wavelength need not actually be equal to zero for the ray
– optics theory to be useful. As long as the light waves propagate through and
round objects whose dimensions are much greater than the wavelength, the
ray theory suffices for describing most phenomena. Because the wavelength
of visible light is much shorter than the dimensions of the visible objects en-
countered in our daily lives, manifestation of the wave nature of light are not
apparent without careful observation.
Ray optics is the simplest theory of light. Light is described by rays that travel
in different optical media in accordance with a set of geometrical rules. Ray
optics is therefore called Geometrical optics. Ray optics is an approximate
theory. Although it adequately describes most of our daily experiences with
light, there are many phenomena that ray optics does not adequately describe.
Ray optics is concerned with the location and direction of light rays. It is there-
fore useful in studying image formation – the collection of rays from each
1
2. point of an object and their redirection by an optical component onto a cor-
responding point of an image. Ray optics permits us to determine conditions
under which light is guided within a given medium, such as a glass fiber. In
isotropic media, optical rays point in the direction of the flow of optical ener-
gy. Ray bundles can be constructed in which the density of rays is proportion-
al to the density of light energy. When light is generated isotropically from a
point source, for example, the energy associated with the rays in a given cone
is proportional to the solid angle of the cone. Rays must be traced through an
optical system to determine the optical energy crossing a given area.
Optical components are often centered about an optical axis, around which
the rays travel at different inclinations. Rays that make small angles (such that
) with the optical axis of a mirror or a lens are called paraxial rays.
In the paraxial approximation, where only paraxial rays are considered, a
spherical mirror, for example, has a focusing property like that of the parabo-
loidal mirror and an imaging property like that of elliptical mirror. The body
of rules that results from this approximation forms paraxial optics, also
called first – order optics or Gaussian optics.
The change in the position and inclination of a paraxial ray as it travels
through an optical system can be efficiently described by the use of a
. This algebraic tool is called matrix optics.
SPHERICAL BOUNDARIES AND LENSES - IMAGE FORMATION
The refraction of rays from a spherical boundary of radius R between two me-
dia of refractive indices n1 and n2 can be examined. By convention, R is posi-
tive for a convex boundary and negative for a concave boundary. By using
Snell’s law, and considering only paraxial rays making small angles with the
axis of the system so that , the following properties may be shown to
hold:
A ray making an angle with the z axis and meeting the boundary at a
point of height y (see figure 1-a) refracts and changes direction so that
the refracted ray makes an angle with the z axis,
All paraxial rays originating from a point in the z=z1 plane
meet at a point in the z=z2 plane, where:
2
3. And
The z=z1 and z=z2 planes are said to be conjugate planes. Every point in
the first plane has a corresponding point (image) in the second with
magnification Negative magnification means that the
image is inverted. By convention, P1 is measured in a coordinate sys-
tem pointing to the left and P2 in a coordinate system pointing to the
right (e.g., if P2 lies to the left of the boundary, then z2 would be nega-
tive).
Figure 1: Refraction at a convex spherical boundary (R>0)
It is worth to indicate here that the image formation properties de-
scribed above are approximate. They hold only for paraxial rays. Rays
3
4. of large angles do not obey these paraxial laws; the deviation results in
image distortion called aberration.
A spherical lens is bounded by two spherical surfaces. It is, therefore, defined
completely by the radii of curvatures R1 and R2 of
its two surfaces, its thickness , and the refractive
index n of its material (figure 2). A glass lens in air
can be regarded as a combination of two spherical
boundaries, air – to – glass and glass– to – air.
A ray crossing the first surface at height y and an-
gle with the z axis (figure 3-a) is traced by ap-
plying equation 1 at the first surface to obtain the
inclination angle of the refracted ray, which is ex-
tended until it meets the second surface. Then eq- Figure 2: A biconvex spherical lens
uation 1 is used once more with
replacing to obtain the in-
clination angle of the ray af-
ter refraction from the second
surface. The results are in gen-
eral complicated. When the lens
is thin, however, it can be as-
sumed that the incident ray
emerges from the lens at about a
the same height y at which it en-
ters.
Under this assumption, the fol-
lowing relations follow:
The angles of the re-
fracted and incident rays
are related by:
Where f, the focal length, is giv- b
en by: Figure 3: (a) Ray bending by a thin lens. (b) Image forma-
tion by a thin lens
4
5. All rays originating from a point meet at a point
(figure 3-b), where:
And
This means that each point in the z=z1 plane is imaged onto a corresponding
point in the z=z2 plane with a magnification factor The focal length f of
a lens therefore, completely determines its effect on paraxial rays.
As indicated earlier, P1 and P2 are measured in coordinate system pointing to
the left and right, respectively, and the radii of curvatures R1 and R2 are posi-
tive for convex surfaces and negative for concave surfaces. For the biconvex
lens shown in figure 2, R1 is positive and R2 is negative, so that the two terms
of equation 5 add and provide a positive f.
Matrix Optics
Matrix optics is a technique for tracing paraxial rays. The rays are assumed to
travel only within a single angle, so that the formalism is applicable to systems
with planar geometry and to meridional rays in circularly symmetric systems.
A ray is described by its
position and its angle with
respect to the optical axis.
These variables are altered axis
as the ray travels through
the system. In the paraxial
approximation, the posi-
tion and angle at the input Figure 4: A ray is characterized by its coordinate and its angle
and output planes of an
optical system are related by two linear algebraic equations. As a result, the
optical system is described by a matrix called the ray – transfer matrix.
The convenience of using matrix methods lies in the fact that the ray – trans-
fer matrix of a cascade of optical components (or systems) is the product of
the ray transfer matrices of the individual components (or systems). Matrix
5
6. optics therefore provides a formal mechanism for describing complex systems
in the paraxial approximation.
The Ray – Transfer Matrix
Consider a circularly symmetric optical system formed by refracting and re-
flecting surfaces all centered about the same axis (optical axis). The z axis lies
along the optical axis and points in the general direction in which the rays tra-
vel. Consider rays in a plane containing the optical axis; say the y-z plane. We
proceed to trace a ray as it travels through the system, i.e., as it crosses the
transverse planes at different axial distances. A ray crossing the transverse
plane at z is completely characterized by the coordinate y of its crossing point
and the angle (figure 4).
An optical system is a set of optical components placed between two trans-
verse planes at z1 and z2, referred to as the input and output planes, respec-
y
Input
plane
1
Output
plane
2
y1 y2
Optical
Z1 Z2 z axis
Optical
system
Figure 5: A ray enters an optical system at position and angle and leaves at position and angle .
tively. The system is characterized completely by its effect on an incoming
ray of arbitrary position and direction . It steers the ray so that it has
new position and direction at the output plane (figure 5).
In the paraxial approximation, when all angles are sufficiently small so that
, the relation between and is linear and can generally
be written in the form:
6
7. Where A,B,C and D are real numbers. Equations 1 and 2 may be conveniently
written in matrix form as:
The matrix M whose elements are A, B, C, D, characterizes the optical system
completely since it permits to be determined for any . It is
known as the ray – transfer matrix.
It is handy to note that all ABCD matrices, for individual elements or a compli-
cated optical system, have the property:
This relation can be utilized as a check on one’s calculation after multiplying
together a long chain of matrices.
Matrices of Simple Optical Components
Free – Space Propagation Since rays travel in free space along straight lines, a
ray traversing a distance d is altered in accordance with and
. The ray – transfer matrix is therefore:
d
Refraction at a Planar Boundary
At a planar boundary between two media of refractive indices n1 and n2, the
ray angle changes in accordance with Snell’s law . In the
paraxial approximation, . The posi-
tion of the ray is not altered, . The ray –
transfer matrix is:
n1 n2
7
8. Refraction at a Spherical Boundary
The relation between and for paraxial rays at a spherical boundary be-
tween two media is provided by equation 1. The ray height is not altered,
. the ray – transfer matrix is:
R
Convex, R > 0; n1 n2
concave, R < 0
Transmission through a thin lens
The relation between and for paraxial rays transmitted through a thin
lens of focal length f is given in equation 5. Since the height remains
unchanged,
f
Convex, f> 0 ; concave, f< 0
Reflection from a planar mirror
Upon reflection from a planar mirror, the ray position is not altered,
. Adopting the convention that the z axis points in the general direc-
tion of travel of the rays, i.e., toward the mirror for the incident rays and away
from it for the reflected rays, thus , its concluded that . The ray –
transfer matrix is, therefore, the identity matrix:
z
z
8
9. Reflection from a spherical mirror
Using equation 1, and the convention that the z axis follows the general direc-
tion of the rays as they reflect from mirrors, one can similarly obtain:
-R
Concave, R< 0; convex, R>0
Note the similarity between the ray – transfer matrices of a spherical mirror
and a thin lens. A mirror with radius of curvature R bends rays in a manner
that is identical to that of a thin lens with focal length .
MATRICES OF CASCADE OPTICAL COMPONENTS
The ray transfer matrix of an optical system composed of a cascade of optical
components whose ray - transfer matrices are M1, M2,…., MN is equivalent to a
single optical component of ray – transfer matrix M. Thus:
M1 M2 MN M= MN…….M2 M1
….
Note the order of multiplication: The matrix of the system that is crossed by
the rays first is placed to the right, so that it operates on the column matrix of
the incident ray first.
Examples:
1. A Set of Parallel Transparent Plates: consider a set of N parallel planar
transparent plates of refractive indices and thicknesses
placed in air (n=1) normal to the z axis. Show that the
ray – transfer matrix is:
9
10. Note that the order of placing the plates does not affect the overall ray – trans-
fer matrix. What is the ray – transfer matrix of an inhomogeneous transparent
plate of thickness do and refractive index n (z)?
Since the ray – transfer matrix of the free space is given by:
Here, the light propagates in a transparent plate of thickness d and refractive
index n. Thus, the distance of propagation of the light in each plate is equal to
the ratio of the optical path to the refractive index of the medium, i.e.,
The ray – transfer matrix of the given optical system is:
In the inhomogeneous medium, the refractive index is function of position
(i.e., it does not have the same value in the various parts of the medium).
Therefore, the ray – transfer matrix of an inhomogeneous transparent plate of
thickness do and refractive index n (z) can be given as follows:
2. A Gap Followed by a Thin Lens: show that the ray – transfer matrix of a
distance d of free space followed by a lens of focal length f is :
10
11. 3. Imaging With a Thin Lens: Derive an expression for the ray – transfer
matrix of a system composed of free space /thin lens/free space, as illu-
strated in the figure. Show that if the imaging condition
is satisfied, all rays originating from a single point
in the input plane reach the output plane at a single point y2, regardless
of their angles. Also show that if d2=f, all parallel incident rays are fo-
cused by the lens onto a single point in the output plane.
To determine the ray – transfer matrix of the thin lens, we refer to the follow-
ing figure.
For thin biconvex lens:
For the above condition to be met (i.e.,
), the constant A must be equal
to 1 and B must be equal to 0.
For ray:
11
12. For ray:
Therefore, the ray – transfer matrix of the thin biconvex lens will be:
If d2=f=image distance, then the ray transfer matrix of the optical system will
be:
4. Imaging With a Thick Lens: consider a glass lens of refractive index n,
and two spherical surfaces of equal radii of curvatures R (figure 5). De-
termine the ray – transfer matrix of the system between the two planes
at distance d1 and d2 from the vertices of the lens. The lens is placed in
air (refractive index =1). Show that the system is an imaging system (i.e.,
the input and output planes are conjugate)if:
Where:
And:
12
13. The points F1 and F2 are known as the front and back focal points, respective-
ly. The points P1 and P2 are known as the first and second principal points,
respectively. The radii of curvatures of the lens’s two spherical surfaces R1
and R2 are taken positive for spherical surface facing to the right (R1) and neg-
Figure 5: Imaging with a thick lens. P1 and P2 are the principal points and F1 and F2 are the focal points.
ative for spherical surface facing to the left (R2). Show the importance of these
points by tracing of rays that are incident parallel to the optical axis.
The ray – transfer matrix of the system between the two planes at distance d1
and d2 from the vertices of the lens is given by:
The ray – transfer matrix of the thick lens is equal to the product of the ray –
transfer matrices of two refracting surfaces of the lens and the distance doptical
traversed by light. Thus:
1. Ray – Transfer Matrix of a Lens System: Determine the ray – transfer
matrix for an optical system made of a thin convex lens of focal length f
13
14. and a thin concave lens of focal length –f separated by a distance f. Dis-
cuss the imaging properties of this composite lens.
The ray – transfer matrix of the current optical system will be:
To demonstrate the imaging properties of such optical system we will consid-
er the following input matrix:
+f -f
When the above Mststem matrix works on
Minput the output will be:
Output=matrix of the system * the input
d=f
This means that the image is real, inverted (due to the minus sign), and minia-
ture.
References
1. D. C. O’Shea, Elements of Modern Optical Design, Wiley, New York, 1985.
2. R. Kingslake, Optical System Design, Academic Press, New York, 1983.
3. Matrix Method in Optics, , Wiley, New York, 1978.
14