By Ziad Helou and Louay Mardini École the Dauversière, Montreal, June 2001 Translated from French...

By Ziad Helou and Louay Mardini École the Dauversière, Montreal, June 2001

Translated from French to English by Nigel Ward

Once upon a time, long, long ago,

scientists discovered something

which is used these days in many branches

of industry and technology .

Once upon a time, long, long ago,

scientists discovered something

which is used these days in many branches

of industry and technology .

Once upon a time, long, long ago,

scientists discovered something which is used these days in many branches

of industry and technology .

Once upon a time, long, long ago,

scientists discovered something

which is used these days in many branches

of industry and technology .

Once upon a time, long, long ago,

scientists discovered something

which is used these days in many branches

of industry and technology ..

this discovery is ...

What is it?

How does it work? How is it used?

A lens is an optical system which makes light converge or diverge.

There are two main families of lenses: There are two main families of lenses:

These lenses are thicker at the centre than at the

edge.

These lenses are thinner at the centre than at the

edge.

It’s much simplerthan I thought!

To understand the functioning of a lens, it’s necessary to first understand the phenomenon of refraction.

glass prism (transparent)

Airprism

Air

= light ray

trajectory without refraction

trajectory without refraction

(Click on ‘refraction’ or ‘trajectory without refraction’ to have their definitions.)

Refraction: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:trajectory without refraction:

It is the normal trajectory of the light when it has not been refracted.

It’s transparentlyobvious!

As their name indicates, these are lenses which converge the light, in other words, direct it towards a common point.

Example:

converging lens

Source of light

click here to turn on the source.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

Common point

As their name indicates, these are lenses which make light converge, in other words, direct it towards a common point.

The converging action of a lens can be explained by considering the lens to be made up of prisms :

upright triangular prismupright triangular prism

inverted triangular prisminverted triangular prism

= light rays

trajectory without refraction

trajectory without refraction

No refraction because the ray arrives on the principal axis.

rectangular prismrectangular prism

It is for this reason that we use the following symbol to converging lenses:

symbol

1.1. the different types of converging lenses1.1. the different types of converging lenses1.1. the different types of converging lenses1.1. the different types of converging lenses

Biconvex Plano-convex Converging meniscus

principal focus principal focus

object

image

principal axis

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.

converging lens

Here’s how to trace the image of a converging lens.

C

1.2. The image of a converging lens: 1.2. The image of a converging lens:

principal focusF'

principal focusF

object

image

principal axis

converging lens

C : optical centre

a

b

a'

b'

CF = CF' = focal lengthCF = CF' = focal length

1.2. The image of a converging lens:1.2. The image of a converging lens:

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.

case 1: the object is at infinity.

F' F

principal axis

converging lens

the image is a point at the principal focus.

2F'

1.3. The different cases of image formation by a converging lens:1.3. The different cases of image formation by a converging lens:

C

The distance CF is called the focal length of the lens.

F' F

principal axis

converging lens

2F'

case # 2: the object is at more than 2 f (f is the focal length).

the image is real, inverted and smaller than the object.

F' F

principal axis

converging lens

2F'

case # 3: the object is at 2 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.

F' F

principal axis

converging lens

2F'

case # 4: the object is between l f and 2 f.

the image is real, inverted and bigger than the object.

F' F

principal axis

converging lens

2F'

case # 5: The object is at the principal focus.

There is no image.

F' F

principal axis

converging lens

case # 6: the object is between the principal focus and the lens.

We extend the refracted rays with virtual rays.

the image is virtual, bigger than the object and on the same side as the object.

Prolongations

Located at the point the virtual rays meet.

Converging lens simulation

Converging lenses are used in spectacles (for short-sightedness) and in magnifying glasses, but they are combined with diverging lensesin several other devices such as cameras, microscopes, telescopes and binoculars ...

Images of some of these devices:

diverging or converging lenses

converging lensConverging

System of lenses

system of lenses

Convergingsystem of lenses

1.4. Uses of converging lenses:1.4. Uses of converging lenses:

Example:

light source

Click here to turn on the source.

diverging lens

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.

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.

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.

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.

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.

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.

Just as with converging lenses, one can explain thedivergence of light by considering its refraction in the prisms .

invertedinverted triangular triangular prismprism

upright triangular prismupright triangular prism

= light rays

Trajectory without refraction

Trajectory without refraction

No refraction because the ray Arrives on the principal axis.

rectangular prismrectangular prism

It’s for this reason that we give the following symbol to diverging lenses:

symbol

Biconcave Plano-concave diverging meniscus

2.1. The different types of diverging lenses :2.1. The different types of diverging lenses :

As a diverging lens does not have the same properties As a diverging lens does not have the same properties as a converging lens, it is evident that the image will as a converging lens, it is evident that the image will not be formed in the same way. not be formed in the same way.

,kytk7t6kuykukuk

2.2. The image formed by a diverging lens: 2.2. The image formed by a diverging lens:

principal axis

diverging lens

principal focus principal focus

Attention, the foci are reversed!Attention, the foci are reversed!

principal axis

diverging lens

principal focus principal focus

object

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.

The image is thus always The image is thus always virtualvirtual, , uprightupright and and smaller smaller than the objectthan the object, just as you observed on the preceding , just as you observed on the preceding slide.slide.

principal axis

diverging lens

principal focus principal focus

object

2.3. The only case of image formation by a diverging lens:2.3. The only case of image formation by a diverging lens:

Diverging lens simulation

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:

diverging or converging lenses

Convergingsystem

system of lenses

Convergingsystem

2.4. Uses of diverging lenses:2.4. Uses of diverging lenses: