Michelson's interferometer uses the principle of division of amplitude to create interference fringes. Light from a source is split into two beams using a half-silvered beam splitter. The beams travel different paths and reflect off mirrors before recombining, creating an interference pattern of fringes. The shape and spacing of the fringes depends on the relative positions and orientations of the mirrors. Michelson's interferometer can be used to measure small changes in distance and determine the wavelength of monochromatic light by counting the number of fringes that shift when a mirror is moved a known amount.
Reflection and Refraction of Optical Rays.
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Presentation of Polarization of Light.
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This presentation is in the Optics folder.
The term Diffraction has been defined by Sommerfield as any deviation of light rays from rectilinear paths which cannot be interpreted as reflection or refraction.
For comments please connect me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com. This presentation is in the Optics folder.
Reflection and Refraction of Optical Rays.
For comments, please contact me at solo.hermelin@gmail.com.
For more presentations on different topics visit my website at http://www.solohermelin.com.
This presentation is in the Optics folder.
Presentation of Polarization of Light.
Please send comments to solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
This presentation is in the Optics folder.
The term Diffraction has been defined by Sommerfield as any deviation of light rays from rectilinear paths which cannot be interpreted as reflection or refraction.
For comments please connect me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com. This presentation is in the Optics folder.
Interference is the superposition of two or more waves producing a resultant disturbance that is the sum of the overlapping wave contribution.
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A few Figures were not downloaded. I recommend to see the presentation on my website in Optics folder.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
This article speaks about the optical phenomenon of diffraction. The terms related to it. This article explains the principle of diffraction and provides a comprehensive understanding for the students of optics.
This article describes the principle and phenomenon of polarization of light. This article also illustrates on Birefringence, Dichroism and crossed polarizers.
Malu's Law is elaborated here as prerequisite to understand Polarization along with Brewster's Angle. Polarization by reflection and polarization by refraction are also discussed here for quick comprehension of the readers.
This article discusses the basics of Interference phenomenon of light. Young's Double Slit Experiment is discussed to understand the phenomenon of Interference and also to understand the wave behaviour of light. Newton's Ring experiment, Lloyd's Mirror experiment, Fresnel's Biprism experiment are studued here to establish the wave nature of light. Also the bright and the dark fringes and there mathematical expressions are elaborated here in this article.
Interference is the superposition of two or more waves producing a resultant disturbance that is the sum of the overlapping wave contribution.
For comments please contact me at solo.hermelin@gmail.com.
A few Figures were not downloaded. I recommend to see the presentation on my website in Optics folder.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
This article speaks about the optical phenomenon of diffraction. The terms related to it. This article explains the principle of diffraction and provides a comprehensive understanding for the students of optics.
This article describes the principle and phenomenon of polarization of light. This article also illustrates on Birefringence, Dichroism and crossed polarizers.
Malu's Law is elaborated here as prerequisite to understand Polarization along with Brewster's Angle. Polarization by reflection and polarization by refraction are also discussed here for quick comprehension of the readers.
This article discusses the basics of Interference phenomenon of light. Young's Double Slit Experiment is discussed to understand the phenomenon of Interference and also to understand the wave behaviour of light. Newton's Ring experiment, Lloyd's Mirror experiment, Fresnel's Biprism experiment are studued here to establish the wave nature of light. Also the bright and the dark fringes and there mathematical expressions are elaborated here in this article.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
8. Temporal & Spatial Coherence
Temporal Coherence Spatial Coherence
The type of coherence related with time The type of coherence related with position
It is known as longitudinal coherence. It is known as transverse coherence.
The temporal coherence of light is related
to frequency bandwidth of the source.
monocromaticity
Spatial coherence is related to size of light
source
9. Interference Of Light
I = A^2
Interference is the phenomenon in which two waves superpose to form the resultant
wave of the lower, higher or same amplitude.
12. Thin Film Interference
When the light is made incident on this thin
film partial reflection and partial refraction
occur from the top surface of the film. The
refracted beam travels in the medium and
again suffers partial reflection and partial
refraction at the bottom surface of the film.
In this way several reflected and refracted
rays are produces by a single incident ray. As
they moves are superimposed on each other
and produces interference pattern.
Stokes treatment : When a beam is reflected from a denser
medium, a path change of λ /2 (or phase π ) occur for the ray.
1 2
3 4
5
6
13. Interference in Parallel Film
( Reflected Rays)
Consider a thin film of uniform
thickness ‘t’ and refractive
index bounded between air. Let us
consider monochromatic ray AB is made
incident on the film, at B part of ray is
reflected (R1) and a part is refracted
along BC. At C The beam BC again suffer
partial reflection and partial
refraction, the reflected beam CD
moves again suffer partial reflection
and partial refraction at D. The
refracted beam R2 moves in air. These
two reflected rays R1 and R2 interfere
to produce interference pattern.
15. Stokes treatment : when a beam is reflected
from a denser medium (ray R1 at B), a path
change of λ /2 (or phase π ) occur for the ray.
Assignment
Shape of the fringes when
t= λ/4 , λ/2 and λ
Hint: Haidinger fringes
16. Special Case
When angle of incident is 90 degree then
Angle of refraction r =0
Assignment:
Condition for constructive and destructive interference in case of reflected.
What will be the pattern of fringes when observed from transmitted side.
17. Interference in Wedge Shaped Film
(Reflected Rays)
The wedge shaped film has a thin
film of varying thickness, having
thickness zero at one end and
increases at the other. The angle of
wedge is θ.
18. Stokes treatment : When a beam is reflected
from a denser medium (ray R1 at B), a path
change of λ /2 (or phase π ) occur for the ray.
19. Special Case
When angle of incident is 90 degree and θ or small angles.
Angle of refraction r=0 and θ= 0 (approx.), (r+ θ) 0
Cos (r+ θ)= cos 0 =1
Condition for constructive and destructive interference : Assignment
20. Thin film neither parallel nor wedge
Assignment:
What will be the shape of the fringe
when the slit is neither parallel nor
wedge shaped
Hint: Fizeau fringes
21. Unit – 1
Wave Optics
1. Newton’s Ring’s
2. Michelson’s Interferometer
3. Fraunhofer Diffraction ( Single slit)
4. Diffraction Grating
5. Rayleigh criterion for limit of resolution
22. Newton’s Ring’s ( History)
• It is named after Isaac Newton, who investigated
the effect in his 1704 treatise Opticks.
23. Newton’s Ring’s
Introduction
The formation of Newton’s Ring’s is an important
application of interference of
Light wave from opposite
faces of a thin film of variable
thickness.
Newton’s Ring’s
1. Reflected light
2. Transmitted light.
26. Theory Explained
When a Plano convex lens of long focal length is placed in contact on a plane glass
plate, a thin air film is enclosed between the upper surface of the glass plate and
the lower surface of the lens. The thickness of the air film is almost zero at the
point of contact O and gradually increases as one proceeds towards the periphery
of the lens. Thus points where the thickness of air film is constant, will lie on a
circle with O as center. By means of a sheet of glass G, a parallel beam of
monochromatic light is reflected towards the lens L. Consider a ray of
monochromatic light that strikes the upper surface of the air film nearly along
normal. The ray is partly reflected and partly refracted as shown . The ray refracted
in the air film is also reflected partly at the lower surface of the film. The two
reflected rays, i.e. produced at the upper and lower surface of the film, are
coherent and interfere constructively or destructively. When the light reflected
upwards is observed through microscope M which is focused on the glass plate,
series of dark and bright rings are seen with center as O. These concentric rings
are known as " Newton's Rings ". At the point of contact of the lens and the glass
plate, the thickness of the film is effectively zero but due to reflection at the lower
surface of air film from denser medium, an additional path of λ/2 is introduced or
phase π (Stokes treatment). Consequently, (In reflected) the center of Newton
rings is dark due to destructive interference.
27. Formation of Newton’s Ring’s
• Newton’s Ring’s In reflected light
Optical path difference
between two successive
reflected waves QS1R1
and NS2R2
= 𝟐μ𝒅 ± 𝝀/𝟐….(1)
(refer: Interference in Wedge –Shaped Film
Note : In wedge thickness is t )
• d= thickness of the air film at N and 𝜆/2 is the
additional path difference due to reflection at G.
28. Condition for constructive interference:
𝟐μ𝒅 = odd multiple of 𝝀/𝟐
𝟐μ𝒅=(𝟐𝒎 + 𝟏)𝝀/𝟐 {or (𝟐𝒎 - 𝟏)𝝀/𝟐 }…. (2) , Where 𝒎 = 𝟎, 𝟏, 𝟐,
Condition for destructive interference :
𝟐μ𝒅= even multiple of 𝝀/𝟐
𝟐μ𝒅 =𝟐𝒎.𝝀/𝟐 …… (3) , Where 𝒎=𝟎,𝟏,𝟐,𝟑
A fringe of a given order (m) will be along the
loci of points of equal film thickness (d) and
hence the fringe will be circular.
29. From fig
QQ1 is the radius of mth order bright or dark ring
𝐐𝐐𝟏=𝐫𝐦
R= radius of curvature of the convex surface.
Since 𝑹≫𝒅 , we can write,
30. From eqn. 5 and 6 we can conclude that the radius of
bright and dark rings is proportional to the square
root of odd natural numbers and natural numbers
respectively.
31. Central Fringe:
At the point of contact of lens and glass
plate d=0. So from equation
the condition for destructive interference
will be satisfied with m=0. This indicates
that the central fringe is dark and appears
as dark spot.
As D= 2 r
32. Application of Newtons Ring
Where 𝒎=𝟎,𝟏,𝟐,𝟑 , and
p = Any fixed (+) integer..1,2,3…… ( Discuss in Experiment in detail) V.Imp
(Also try from dark fringes)
34. Newton’s ring’s with transmitted light:
Newton’s ring can also be observed with transmitted
light. There are two differences in the reflected and
transmitted systems of rings-
1. The rings in transmitted light are exactly
complementary to those seen in the reflected
light, so that the central spot is now bright.
1. The rings in transmitted light are much
poorer in contrast than those in reflected
light.
35. Numerical’s
Question: In a Newton's ring experiment the diameters of 4th and 12th dark rings
are 0.4 cm and 0.7 cm respectively. Deduce the diameter of 20th dark ring.
Ans: In Newton's ring experiment.
Given that:
m= 4; (m+p)=12, p=8
Dm = 0.4 cm and D m+p =0.7 cm.
The wavelength of sodium light using Newton's ring is
λ = D²m+p - Dm²/4pR
4λR = D²m+p - Dm²/p
4λR =(0.7)²-(0.4)²/p……(1)
We know that the diameter of the dark ring in presence of air is
Dm² = 4mλR
D20² = 20 X (4λR)……(2)
Putting the value of 4λR from Eq (1) in Eq (2)
D20² = 20 X [(0.7)²- (0.4)²]/8
D20= 0.91 cm.
36. Question: In a Newton's ring set up, diameter of 20th dark ring is found to be
7.25mm. The space between spherical surface and the flat slab is then filled
with water (μ= 1.33). Calculate the diameter of the 16th dark ring in new set
up.
Ans. Given that : D20= 7.25 mm
We know that the diameter of mth ring in presence of air is
Dm² = 4mλR
D20² =4 X 20 X λR
4λR= (7.25)²/20……………………………(1)
New set up:
Now liquid is introduced, then diameter of the ring is
D`m² = 4mλR/μ
D`16²= 4 X 16 X λR/1.33
= 16 X (4λR)/1.33…………………………..(2)
Putting the value of 4λR from equation (1) in (2)
We get,
D`16²= 16 X (7.25)²/20 X 1.33
D`16 = 5.62 mm.
40. Conclusion
Einstein : "If the Michelson–Morley experiment had not brought
us into serious embarrassment, no one would have regarded the
relativity theory as a (halfway) redemption
41. Interferometer
• Interferometers are investigative tools used in
many fields of science and engineering. They are
called interferometers because they work by
merging two or more sources of light to create an
interference pattern, which can be measured and
analyzed; hence 'Interfere-o-meter', or
interferometer.
42. MICHELSON’S INTERFERROMETER
Principle:- The MI works on the principle of division of amplitude. When the incident
beam of light falls on a beam splitter which divided light wave in two part in different
directions. These two light beams after traveling different optical paths, are
superimposed to each other
and due to superposition interferences fringes formed.
(Image of M2)
43. Construction:- It consists of two highly polished plane mirror M1 and M2, with
two optically plane glass plate G1 and G2 which are of same material and same
thickness. The mirror M1 and M2 are adjusted in such a way that they are
mutually perpendicular to each other. The plate G1 and G2 are exactly parallel to
each other and placed at 45° to mirror M1 and M2. Plate G1 is half silvered from
its back while G2 is plane and act as compensating plate. Plate G1 is known as
beam-splitter plate.
The mirror M2 with screw on its back can slightly titled about vertical and
horizontal direction to make it exactly perpendicular to mirror M1. The mirror M1
can be moved forward or backward with the help of micrometer screw and this
movement can be measured very accurately.
Working: Light from a broad source is made parallel wavefront by using a convex lens L.
Light from lens L is made to fall on glass plate G1 which is half silver polished
from its back. This plate divides the incident beam into two light rays by the
partial reflection and partial transmission, known as Beam splitter plate. The
reflected ray travels towards mirror M1 and transmitted ray towards mirror M2.
These rays after reflection from their respective mirrors meet again at 'O' and
superpose to each other to produce interference fringes. This firings pattern is
observed by using telescope.
Functioning of Compensating Plate: In absence of plate G2 the reflected ray passes
the plate G1 twice, whereas the transmitted ray does not passes even once.
Therefore, the optical paths of the two rays are not equal. To equalize this path the
plate G2 which is exactly same as the plate G1 is introduced in path of the ray
proceeding towards mirror M2 that is why this plate is called compensating plate
because it compensate the additional path difference.
44. Formation of fringes in MI
When the mirror M1 and
the virtual image M2ꞌ of M2
are not exactly parallel
localized fringes are produced.
When the mirror M1 and
the virtual image M2ꞌ of M2
are not exactly parallel
localized fringes are produced.
Assignment
Shape of the fringes when
d= λ/4 ,λ/2 and λ
45. The shape of fringes in MI depends on inclination of mirror M1 and M2. Circular fringes
are produced with monochromatic light, if the mirror M1 and M2 are perfectly
perpendicular to each other. The virtual image of mirror M2 and the mirror M1 must be
parallel. Therefore it is assumed that an imaginary air film is formed in between mirror
M1 and virtual image mirror M'2. Therefore, the interference pattern will be obtained due
to imaginary air film enclosed between M1 and M’2.From Fig. if the distance M1 and M2
and M'2 is 'd', the distance between S'1 and S'2 will be 2D.
If the light ray coming from two virtual sources
making an angle θ with the normal then the path
difference between the two beams from S1 and S2
will becomes
As one of the ray is reflecting from denser medium
mirror M1, a path change of λ/2 occurs in it (Stokes treatment).
Hence the effective path difference between them will be
Formation of Circular Fringes:
46. Where d and λ are constants, so θ will be constant for given order number (m). Hence
maxima will be in the form of concentric circles about the foot of the perpendicular from
the eyes to the mirror as a common center.
For Small angle θ
This type of fringes are called fringe of equal inclination.
Fringes are non-localized and situated at infinity.
47. Formation of Localized fringes:
• When the mirror M1 and the virtual image M2ꞌ of M2 are not exactly parallel localized
fringes are produced.
48. Application of Michelson Interferometer
• Determination of Wavelength of a monochromatic light:
For this purpose the interferometer is adjusted to obtain circular fringes in the field of view of the
observing telescope. Then the mirror M1 is through a distance λ/2. The path difference will be
changed by 2× λ/2= λ and hence the position of a bright fringe is taken by the next bright one.
Let, position of M1 is shifted by a distance x until N bright fringes cross the cross-wire of the
observing telescope.
Therefore, 𝒙=N𝝀/𝟐
𝝀=𝟐𝒙/N
Now, x can be measured with the help of a micrometer screw. Thus by counting m we can find
out λ.
49. Q.1. In MI 200 fringes cross the field of view when the movable mirror is displaced
through 0.05896mm. Calculate the wavelength of the monochromatic light used.
Solution:- Given
N=200
x= 0.05896mm = 0.05896 X 10-3 m
So the wavelength
50. Determination of difference in Wavelength:
If the source emits the light of two wavelengths λ1 and λ2 (λ1> λ2) then each wave will produce
an interference system of its own. In this situation if M1 is displaced, the field will be alternately
distinct and indistinct. The fringes will be in consonance when the bright rings of one wave
coincide with the bright ring of another. Similarly the fringes will be in dissonance bright ring of
one wave coincide with the dark ring of another.
Let mirror M1 is displaced by a distance d so that the fringes pass from one consonance to next
consonance through the intermediate state of dissonance. This will happen when value of d is
such that.
Where m and (m+1) represents the number of fringe shift for the light of wavelength 𝜆 1and 𝜆2.
If 𝜆1 is known, we can find 𝜆2 from the above relation. Then difference in wavelength can be
determined.
λ =λ1- λ2 = 2 d (λ1. λ2) check
51. Determination of refractive index of a material:
To determine the refractive index of a material (μ), the interferometer is first to be adjusted for
white light fringes when the optical path for two interfering beam are made equal. A thin wire is
attached to the middle of the mirror M1 and the central achromatic fringe with white light is to be
made coincident with the wire.
Now a thin plate (𝑟𝑒𝑓𝑟𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛𝑑𝑒𝑥=μ 𝑎𝑛𝑑 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠=𝑡) is introduced in the path of one of the
interfering rays. An extra optical path (μ−1)𝑡 is introduced in the side of the plate. Since the ray
travels twice though the plate, the path difference introduced is 2(μ−1)𝑡 between the two
interfering beam.
Due to this extra path central fringe will be displaced from the wire. The mirror M1 is then to be
displaced 𝑑 until the central fringe again coincides with the wire. In that case
If thickness of the plate t is known, we can find μ from the above relation.
52. Numerical’s
Question: A thin transparent sheet of refractive index μ =1.6 is introduced in one of the
beams of Michelson interferometer and a shift of 24 fringes for λ= 6000 A° is obtained.
Calculate the thickness of the sheet.
Ans: In Michelson interferometer,
Given that :λ=6000 Å, μ=1.6,
We know that,
2t(μ-1)= 2d …….(1)
2d=mλ , …… (2)
From (1) and (2)
2t(μ-1)=mλ
t= mλ/2(μ-1)
t= 1.2 X 10⁻⁵ m.
53. Diffraction of Light
• Diffraction refers to various phenomena that occur when a wave
encounters an obstacle or a slit. It is defined as the bending of light
around the corners of an obstacle or aperture into the region of
geometrical shadow of the obstacle.
Assignment:
Fresnel Distance
83. Resolving Power
• Resolution: When two objects or their images are very close to
each other they appeared as a one and it not be possible for the
eye to seen them separate. Thus to see two close objects just as
separate is called resolution.
• Limit of resolution: The smallest distance between two
object, when images are seen just as separate is known as limit of
resolution.
• Resolving Power: The ability of an optical instrument to
produce two distinct separate images of two objects located very
close to each other is called the resolution power.
84. Rayleigh Criterion for Resolution
• Lord Rayleigh (1842-1919) a British Physicist proposed a criterion which can
manifest when two object are seen just separate this criterion is called
Rayleigh’s Criterion for Resolution
Well Resolved
Just resolved
Not resolved
85. Resolving power of a telescope
Resolving power of telescope is defined as the reciprocal of the smallest angle sustained at the
object by two distinct closely spaced object points which can be just seen as separate ones
through telescope. Let a is the diameter of objective telescope as shown in fig and P1 and P2 are
the positions of the central maximum of two images. According to Rayleigh criterion these two
images are said to be separated if the position of central maximum of the second images
coincides with the first minimum or vice versa.
The path difference between AP2 and
BP2 is zero and the path difference
between AP1 and BP1 is given by
If dθ is very small sin dθ = dθ
…….. (1)
…….. (2)
For rectangular
aperture
