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ABERRATIONS
Dr.N. LALITHA KUMARI
Lecturer in PHYSICS
Silver Jubilee Govt.,College(A),
KURNOOL
ABOUT LENS
R2
F2
C
f
F1
R1
1
2
2
1
1---marginal rays
2----paraxial rays.
Derivation produced by a thin lens
δ
α
o
h
β
c
u
I
v
From the ▲AIO, δ=α+β
Hence α=tanα and β=tanβ
α= h/u
Now, δ=h/u + h/v
δ=h/v-h/u=h(1/v-1/u)
Or δ=h/f
and β=h/v
since u=-ve and v=+ve
ABERRATIONS
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Definition of Aberrations.
Types of Aberrations.
Chromatic Aberrations.
Monochromatic Aberrations.
Mathematical Analysis & Visuals.
Methods of Elimination.
What is an Aberration?
The deviations or defects observed in
the actual size, position, shape and
colour in the image of an object
formed by a single lens are called
Aberrations.
CAUSE FOR ABERRATIONS
These aberrations are caused due to
the convergence of different rays to
different points.
TYPES OF ABERRATIONS
CHROMATIC ABERRATIONS

Formation of Multicoloured image.

Disability of lens to converge different
colours at different points.
TYPES OF CHROMATIC ABERRATIONS

Longitudinal
The formation of images of different
colours in different positions along the axis

Lateral /Transverse
The defect in images of different
colours are formed of different sizes
perpendicular to the axis .
LONGITUDINAL CHROMATIC ABERRATIONS

Chromatic aberration
of a single lens causes
different wavelengths
of light to have
differing focal
lengths.
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L.C.A.= f r - f v
CALCUALTION OF LONFITUDINAL
CHROMATIC ABERRATION OF A THIN
LENS
(i)When the object is situated at
infinity.
(ii)When the object is situated at a
finite distance.
When the object is situated at infinity
General formulae=
1/f=(µ-1)(1/R1-1/R2),
If fv,fR and fy be the focal length of the lens for violet, red and yellow
1/fv=(µv-1)(1/R1-1/R2), ………..(1)
1/fR=(µR-1)(1/R1-1/R2),……………(2)
1/fY=(µY-1)(1/R1-1/R2)……………….(3)
2 in 1 gives 1/fv-1/fR=(µv-µR)(1/R1-1/R2),
fR-fv =(µv-µR)(µy-1)(1/R1-1/R2),
fv.fR
(µy-1)
BY SOLVING THEM
fR-fv=ώ.fy
WHEN THE IMAGE AT A FINITE DISTANCE THEN
VR-VV=ώ/fV .Vy2
LATERAL/TRANSVERSE CHROMATIC ABERRATIONS
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Origin of transverse chromatic aberration.
The size of the image varies from one color
to the next.
Visual of chromatic aberrations1
VISUAL FOR CHROMATIC ABERRATION 2

Severe purple fringing can be seen at the edges of
the horse's forelock, mane, and ear.
VISUAL FOR CHROMATIC ABERRATION 3

On top is corner detail in
a photograph taken with a
higher quality lens;
bottom is a similar
photograph taken with a
wide angle lens showing
visible chromatic
aberration (especially at
the dark edges on the
right).
VISUAL 4
A cross made by two black match stick mounted on a cork.
Methods of elimination of chromatic aberration
•
•
Achromatic Doublet
A combination of convex lens made up of
by crown glass and concave lens made up of
by flint glass.
Arranging two converging lenses coaxially
Two convex lenses made up of by same
material arranged coaxially at a distance of
d = f1+f2
2
ACHROMATIC DOUBLET
•
For an achromatic
doublet, visible
wavelengths have
approximately the same
focal length.
•
Diffractive optical
element with
complementary
dispersion properties to
that of glass can be used
to correct for color
aberration.
USING TWO CONVEX LENSES

If the distance
between the lenses is
d = f1+f2
2
MONOCHROMATIC ABERRATIONS
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The deviations in the actual size,
shape and position in the image of an
object formed by a single lens, when
the object is illuminated by single
wavelength light.
TYPES OF MONO CHROMATIC ABERRATION
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Spherical Aberrations.
Astigmatism.
Coma.
Distortion.
Curvature.
SPHERICAL ABERRATION
Def. : The failure or inability of the lens to
form a point image of an axial point object.
TYPES :
Longitudinal : the formation of image in
different positions along the axis
Lateral : the formation of image in different
sizes perpendicular to the axis.
VISUAL OF LONGITUDINAL SPHERICAL ABERRATION
Side view and chromatic Airy disc of a bright star at image plan. An asymmetry variation of the Airy disk occurs
around the paraxial focal plane, displaying spherical aberrations
METHODS OF ELIMINATION OF SPHERICAL ABERRATION
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By means of stops.
By using two suitable lenses in
contact.
By using crossed lens.
By using two plano – convex lenses
separated by a distance.
ASTIGMATISM
When a point object is
situated far of the axis of
a lens, the image formed
by the lens is not in a
perfect focus.
It consists two mutually
perpendicular lines
separated by finite
distance.
Side view and Airy disc of a bright star coming 25° off axis showing astigmatism; the tangential and sagittal line image do not
coincide in the area of less conSide view and Airy disc of a bright star coming 25° off axis showing astigmatism; the tangential and
sagittal line image do not coincide in the area of less confusion and in this case display a cross shape.
fusion and in this case display a cross shape
VISUAL OF ASTIGMATISM
Astigmatism as evidenced by the blurring of white dots.
Spoked wheel
Classic example of astigmatism. Left wheel: no astigmatism.
In the presence of astigmatism (middle and right wheels) one
discriminates between the sagittal and tangential foci.
.
ELIMINATION OF SPHERICAL ABERRATIONS
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By using two convex
Lenses coaxially at
a distance
d = f1 – f2
d = f1 – f2
ELIMINATION OF ASTIGMATISM
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USING ANASTIGMAT
By using a convex and a concave lens of
suitable focal lenghs and separated by a
distance . Such a combination is called an
anastigmat.
COMA, "comet" in latin

Coma occurs because off-axis
rays no not quite converge at
the focal plane. Coma is
positive when off-axis rays
focus furthest from the axis,
and negative when they are
closest.
spot diagram showing coma
aberration. The resulting image
takes the shape of a comet.
ELIMINATION OF COMA
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using stops
Abbe condition
µ1Y1SinӨ1 = µ2Y2SinӨ2
Using Aplanatic surface
DISTORTION
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The variation in the
magnifications
produced by a lens
for different axial
distances results in an
aberration called
distortion.
It is of two types.
1.Pin cushion .
2.Barrel shaped.
ORIGIN FOR DISTORTION
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The influence of
stop position on
distortion. Note
that the image
size h differs for
a constant object
size y.
ELIMINATION OF DISTORTION
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A stop is placed in
between two
symmetrical lenses,
so that the pin –
cushion distortion
produced by the first
lens is compensated
by the barrel – shaped
distortion produced
by the second lens.
VISUAL FOR DISTORTION 1
VISUAL FOR DISTORTION 2
Geometric distortion: the photograph does not flatter the
person at the left. (18-mm lens on a 24×36 mm slide)
curvature

The image of an extended
plane object due to a
single lens is not flat one
but will be a curved
surface. The central
portion of the image
nearer the axis is in focus
but outer regions of the
image away from the axis
are blurred.
CURVATURE OF THE FIELD DUE TO
CONVEX LENS
CURVATURE DUE TO CONCAVE LENS
ELIMINATION OF CURVATURE