TD Optique Géométrique Corrigé - Physique-Chimie TSI1
TD2 : Optique géométrique – Corrigé
Exercice 1
P
T
O
P0
T0
O0
l
H
h
d
l=h/2
d=H/2
Exercice 2
βα
α
α
α β= 2α
Exercice 3
I= (x , y , z) x
x −x I1= (−x , y , z)
y z
I3= (−x , −y , −z)
Exercice 4
n
e
i
i2
i2
i3
h
d
(i) =
n(i2) = (i3) i3=i
d=h(i3)'hh=e(i)−e(i2)'
e(i−i2) (i)'i=n(i2)'ni2 d'i×(1 −1/n)e
Exercice 5
I
C
A0
di
r
H
CA0=CH +HA0=R(i) + R(i)/ (r−i) = R((i) +
(i)/ (r−i))
dR
(i)'1 (i)'i (r−i)'r−i
n(i) = r ni =r
CF 0=R×n/(n−1)
r=π/2 n(il)=1 (i) = d/R
dl=R/n
d',
Exercice 6
•(i) = n(r) i=nr
•(i0) = n(r0) i0=nr0
r+r0=A
(i−r) (i0−r0)
D= (i−r)+(i0−r0)
D= (n−1)A
Exercice 7
n(i)=1i (i) =
r/√r2+l2r=d/2
l =√n2−1×d/2
l
Exercice 8
D C
N
BA n
I
i
rr0
i0
r I (r) = n/N r=(n/N)
BC r0=π/2 −r=π/2 −(n/N)
BC
N(r0)<1
(r0) = (π/2 −r) = (r) = q1−2(r) = p1−(n/N)2
√N2−n2<1
α i
i=π/2
(α) = √N2−n2
n α N
n √N2−1< n < N
Exercice 9
C
A
R1
30◦
R2
B
r
i=
(1/1 .5) = ,
i (i) = R/2
R=1
2
i=
r=,
Exercice 10
un peu
h =H−Y d
X
1−(i)
pn2−2(i)
Exercice 11
e
S
S0
S00
d
i
i1 (i)'i (i)'i (i)'1
S0S00 =δ=d
(i)=d
i d=2ei
n
δ=2e
n=,
Exercice 12
O
A
B
A0
B0
F
F0
1
OA0−1
OA =1
f0⇒OA0=,
O
A
B
A0
B0
F
F0
Gt=A0B0
AB =OA0
OA =f0
f0+OA = 4
Exercice 13
(θ0) = AB
f0
2
=f0
1(θ)
f0
2
θ0=f0
1
f0
2
θ
=1
60 G= 100 θ0= 100
',
F1O1O2
F0
2
A1
L1
L2
B1
θθ0
Exercice 14
on ne cache pas une par-
tie de l’image !
O
A
B
A0
B0
FF0
Exercice 15
A0B0
•1
OA1−1
OA =1
f0⇒OA1= 6
•A2 A1 M OA2=−2
•Attention :
F F0
OA2= 2
1
OA0−1
OA2
=1
f0⇒OA0= 1
•
B y=
1 y=−1
−1
F
A
B
A0
B0
L
O
M
F
A
B
A0
B0
L
O
M
FA
B
A0
B0
L
O
M
A0B0
AB A0B0
Exercice 16
(α) = h/d'(α)⇒α'3×10−4
l=P P ×(α)'75 ×10−6= 75 µ
r=Rd
D
r < h R= 1
r=h D =dR
h'3
1
d+1
P R =1
f0 P R =,
1
d+1
P P =1
f0
2
f0
2=,
∆V=1
f0
2−1
f0',δ
1
/
2
100%
