4 Lenses

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Chapter 4 Lenses
By Ziad Helou and Louay Mardini
École the Dauversière, Montreal, June 2001
Translated from French to English by Nigel Ward
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Once upon a time, long, long ago, scientists
discovered something which is used these days
in many branches of industry and technology
.
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(No Transcript)
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(No Transcript)
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Once upon a time, long, long ago, scientists
discovered something which is used these days
in many branches of industry
and technology .
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Once upon a time, long, long ago, scientists
discovered something which is used these days
in many branches of industry and technology
..
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this discovery is ...
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What is it?
THE LENS
How does it work?
How is it used?
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Introduction
A lens is an optical system which makes light
converge or diverge.
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There are two main families of lenses
Converging lenses
Diverging lenses
Its much simplerthan I thought!
These lenses are thicker at the centre
than at the edge.
These lenses are thinner at the centre than at
the edge.
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Refraction
To understand the functioning of a lens, its
necessary to first understand the phenomenon of
refraction.
glass prism (transparent)
light ray
trajectory without refraction
trajectory without refraction
Air
prism
Air
(Click on refraction or trajectory without
refraction to have their definitions.)
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Refraction It is the change of direction of the
light when it crosses the boundary between two
transparent media with different refractive
indices.
trajectory without refraction It is the normal
trajectory of the light when it has not been
refracted.
Its transparently obvious!
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1. Converging lenses
As their name indicates, these are lenses which
converge the light, in other words, direct it
towards a common point.
Example
click here to turn on the source.
converging lens
Source of light
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
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As their name indicates, these are lenses which
make light converge, in other words, direct it
towards a common point.
Common point
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The converging action of a lens can be explained
by considering the lens to be made up of prisms

upright triangular prism
trajectory without refraction
rectangular prism
No refraction because the ray arrives on
the principal axis.
trajectory without refraction
inverted triangular prism
light rays
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It is for this reason that we use the following
symbol to converging lenses
symbol
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1.1. the different types of converging lenses
Biconvex
Plano-convex
Converging meniscus
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1.2. The image of a converging lens
Heres how to trace the image of a converging
lens.
converging lens
object
C
principal axis
principal focus
principal focus
image
any ray parallel to the principal axis gets
refracted through the principal focus.
any ray passing through the principal focus is
refracted parallel to the principal axis.
any ray passing through C (the centre of the
lens) is not refracted.
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1.2. The image of a converging lens
CF CF' focal length
converging lens
b
object
a'
C optical centre
principal axis
a
principal focus F'
principal focus F
image
b'
any ray parallel to the principal axis gets
refracted through the principal focus.
any ray passing through the principal focus is
refracted parallel to the principal axis.
any ray passing through C (the centre of the
lens) is not refracted.
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1.3. The different cases of image formation by a
converging lens
case ? 1 the object is at infinity.
converging lens
principal axis
C
2F'
F'
F
the image is a point at the principal focus.
The distance CF is called the focal length of the
lens.
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case 2 the object is at more than 2 f (f is
the focal length).
converging lens
principal axis
F
F'
2F'
the image is real, inverted and smaller than the
object.
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case 3 the object is at 2 f.
converging lens
principal axis
2F'
F'
F
the image is real, inverted, the same size as the
object and is located at the same distance from
the lens as the object.
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case 4 the object is between l f and 2 f.
converging lens
principal axis
F
2F'
F'
the image is real, inverted and bigger than the
object.
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case 5 The object is at the principal focus.
converging lens
principal axis
F
2F'
F'
There is no image.
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case 6 the object is between the principal
focus and the lens.
We extend the refracted rays with virtual rays.
Prolongations
converging lens
principal axis
F
F'
the image is virtual, bigger than the object and
on the same side as the object.
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Converging lens simulation
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1.4. Uses of converging lenses
Converging lenses are used in spectacles (for
short-sightedness) and in magnifying glasses,
but they are combined with diverging lenses in
several other devices such as cameras,
microscopes, telescopes and binoculars ...
Images of some of these devices
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2. Diverging lenses
In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
diverging lens
Example
Click here to turn on the source.
light source
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In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
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In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
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In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
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In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
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In this case also, as their name indicates, these
are lenses which diverge the light, in other
words, make it spread out more and more.
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Just as with converging lenses, one can explain
the divergence of light by considering its
refraction in the prisms .
inverted triangular prism
Trajectory without refraction
rectangular prism
No refraction because the ray Arrives on the
principal axis.
Trajectory without refraction
upright triangular prism
light rays
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Its for this reason that we give the following
symbol to diverging lenses
symbol
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2.1. The different types of diverging lenses
Biconcave
Plano-concave
diverging meniscus
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2.2. The image formed by a diverging lens
As a diverging lens does not have the same
properties as a converging lens, it is evident
that the image will not be formed in the same
way.
,kytk7t6kuykukuk
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diverging lens
principal axis
principal focus
principal focus
Attention, the foci are reversed!
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diverging lens

object
principal axis
principal focus
principal focus
any ray parallel to the principal axis gets
refracted through the principal focus.
any ray which passes through the principal focus
is refracted parallel to the principal axis.
any ray which passes through C (the centre of the
lens) is not refracted.
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2.3. The only case of image formation by a
diverging lens
diverging lens
object
principal axis
principal focus
principal focus
The image is thus always virtual, upright and
smaller than the object, just as you observed on
the preceding slide.
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Diverging lens simulation
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2.4. Uses of diverging lenses
Diverging lenses are used in spectacles (for
long-sightedness), but they are combined with
converging lenses in several other devices such
as cameras, microscopes, telescopes, binoculars
...
Images of some of these devices