[PDF] Utiliser les distances algébriques en optique





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Utiliser les distances algébriques en optique

A B est placée à 50 cm du centre optique O d'une lentille convergente avec 'A situé sur l'axe optique



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Searches related to distance a zero definition PDF

In R we can use the Euclidean distance to measure the length of the interval from 0 to 1 which has the length 1 Now let’s look at the length of what we have remaining in [01] at each step: Step n (k) Number of subintervals remaining Length of one subinterval Ink total length ? 2n k=1 Ink 0 1 1 1 1 2 1/3 2/3

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    The Manhattan distance, often called Taxicab distance or City Block distance, calculates the distance between real-valued vectors. Imagine vectors that describe objects on a uniform grid such as a chessboard. Manhattan distance then refers to the distance between two vectors if they could only move right angles. There is no diagonal movement involv...

  • Chebyshev Distance

    Chebyshev distance is defined as the greatest of difference between two vectors along any coordinate dimension. In other words, it is simply the maximum distance along one axis. Due to its nature, it is often referred to as Chessboard distance since the minimum number of moves needed by a king to go from one square to another is equal to Chebyshev ...

  • Minkowski

    Minkowski distance is a bit more intricate measure than most. It is a metric used in Normed vector space (n-dimensional real space), which means that it can be used in a space where distances can be represented as a vector that has a length. This measure has three requirements: 1. Zero Vector — The zero vector has a length of zero whereas every oth...

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What is the total distance traveled?

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What is the difference between a zero vector and a positive vector?

Zero Vector — The zero vector has a length of zero whereas every other vector has a positive length. For example, if we travel from one place to another, then that distance is always positive. However, if we travel from one place to itself, then that distance is zero.

What is an example of a set with measure zero?

This Cantor Set in 2D (which has infinitely many points) is another example of a set with measure zero. Figure 2?:MatLab output for n=0,...,4 In the long run the white part of the square will be so thin that it will not take up any area. There will be individual white strings in the carpet, but their area will equal 0.

1. Utiliser les distances algébriques en optique9

1

Utiliser les distances

algébriques en optique - Quand on ne sait pas ŰC omprendre que la notion de distance algébrique est indispensable en optique exe mPle Si u ne image ( ' ')ABO lentille convergente avec 'A distance 'OA

à gauche de la lentille

L a réponse est donnée par la notion de distance algébrique : s i ' 5,0OA cm alors 'A est à droite de O ' 5,0 OA cm alors 'A est à gauche de O (on dit - Que faire ? - ŰIl e st indispensable de connaître les conventions suivantes :

10Couleur, vision et image

sorte que

0AB''0AB

''0AB - Conseils - Les énoncés des exercices donnent des indications qui sont utiles pour connaître - Exemple traité -

Soit la situation suivante :

Les distances algébriques OA, 'OA, AB et ''AB sont-elles positives ou négatives

1. Utiliser les distances algébriques en optique11

ͮSo lution

A et 'A sont à gauche de O donc 0OA et '0OA B est au-dessus de A et 'B est au-dessus de 'A donc 0AB et ''0AB peut pas la former sur un écran mais on peut la voir en regardant à travers la - Exercices -

ExErcicE 1.1

1 2 3

ExErcicE 1.2

la lentille a une distance focale ' 50f

OA'OA''AB'OF

12Couleur, vision et image

ExErcicE 1.3 La m éthode de Sibermann permet de déterminer expérimenta- Dans cette situation on montre que la distance focale est égale à la moitié de la

1 Ȗ

2

3 Combien vaut la distance focale de cette lentille ?

- Pour vous aider à démarrer -

ExErcicE 1.1 OA et 'OA, puis AB et ''AB,

'OF

ExErcicE 1.2

ExErcicE 1.3

1. Utiliser les distances algébriques en optique13

Solutions

- Solutions des exercices -

ExErcicE 1.1

1 Le point A est situé à 6 carreaux à gauche du point O6,0 OA

Le point

'AO' 12,0OA

2 BA2,0AB

'B est 4 carreaux au-dessous de 'A' ' 4,0 AB

3 F est à 4 carreaux à droite de O' ' 4,0 f OF

ExErcicE 1.2

2,00AB

donc

10 OA' ' 50 f OF

' 0,050OA l'image ' 0,050' '2,00 0,01010 OAA B ABOA

OA'OAAB''AB'OF

10 m0,050 m- 0,010 m

ExErcicE 1.3

1

Comme ici

1,00AB cm, on en déduit que ' ' 1,00 ABcm

et ' ' 1,001,001,00 AB AB

2 25 OA' 25OA

3 La distance focale de cette lentille est égale à la moitié de la distance entre la

' 25'12,5 22
OAf

2. Déterminer graphiquement la position et la taille de l'image d'un objet, donnée par une lentille15

2

Déterminer graphiquement

la position et la taille de l'image d'un objet, donnée par une lentille - Quand on ne sait pas ŰRe voir les conventions graphiques (comment représenter un axe optique, une exe mPle OA ci-dessus, si le point A est à gauche du point O alors 0OA

à droite du point

O alors 0OA - Que faire ? - ŰLa r elation entre la distance focale 'fC est : 1'f C avec 'fCį méthode suivante R eprésenter sur le schéma

16Couleur, vision et image

Les foyers de la lentille

F et F' (leurs positions se déduisent de la

distance focale 'f de la lentille : 'f OF' O AB point AB B

B' (B'B

Rayon n° 1 : rayon issu de B

Il sort de la lentille en direction du foyer image F'

B passant par le centre optique O

BF. Il sort de la

B'A'du point A

R elier les points

A' et B'A' vers B'

A'B' relever sa position

OA' et sa taille

A'B' - Conseils - B'

2. Déterminer graphiquement la position et la taille de l'image d'un objet, donnée par une lentille17

- Exemple traité -

A'B' AB, donnée par une lentille

de distance focale

5, m'0 c .f

1 2

ͮSo lution

F et F' Ici ' 5,0f

0OF (F est à gauche de O0OF'

F' est à droite de O

AB

8,0 OAcm et

3,0ABquotesdbs_dbs26.pdfusesText_32
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