24/9/2010 1

Les gens ont des étoiles qui ne sont pas les mêmes.

Pour les uns qui voyagent, elles sont des guides.

Pour les autres, elles ne sont rien que des petites lumières.

Pour d’autres, qui sont savants, elles sont des problèmes.

Le Petit Prince (Antoine de St Exupéry)

24/9/2010 2

(A): Gravitational lensing (B): Optical lens experiment

Deflector plane Observer plane Observer planeLens plane

O1 O1

O2 O2

24/9/2010 3

(A): Gravitational lensing (B): Optical lens experiment

Deflector plane Observer plane Observer planeLens plane

O1 O1

O2 O2

24/9/2010 4

(A): Gravitational lensing (B): Optical lens experiment

Deflector plane Observer plane Observer planeLens plane

O1 O1

O2 O2

24/9/2010 5

r

ni

ε(ξ)

24/9/2010 6

2. Gravitational lenses5. THE OPTICAL GRAVITATIONAL LENS (GL)

EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

Deflection of a light ray passing through an axi-ally symmetric optical lens.

24/9/2010 7

2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

, (5.1)

, (5.2)

, (5.3)

, (5.4)

. (5.5)

r

irin

sinsin

rGMric

2

)(4)(

rdd

cnGM

dd

2)1()(4

00

2ln

1sc

nR

24/9/2010 8

2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

Right: examples of (upper left) a 'point mass' lens (28 cm in diameter) manufactured at the Hamburg Observatory and of (lower right) a 'spiral galaxy' optical lens (30 cm in diameter) produced by the authors at the European Southern Observatory (Garching bei München).

Below: several examples of axially symmetric optical lensessimulating the light deflection properties due to a point mass(a), a SIS galaxy (b), a spiral galaxy (c), a uniform disk (d)and a truncated uniform disk of matter (e).

24/9/2010 9

2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

d / d = -K, (5.6)

() = (0) + K (0 - ). (5.7)

(5.8)

, (5.9)

, (5.10)

0

2 ' ' 'M d

2

02 1 exp / 1/c cc

M

0 exp / c

24/9/2010 10

2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

, (5.11)

M() = 0 2, if c, (5.12a)

M() = 0 c2, if c. (5.12b)

0

2/0 0 0

20 /

8 exp( )ln exp exp( 1)

c

c

c

c c

G z dzzn c

24/9/2010 11

2. Gravitational lenses5. THE OPTICAL GL EXPERIMENT:5.1. Shapes of axially symmetric optical lenses:

if c 0, (5.13a)

(5.13b)

if c. (5.13c)

20 020

4ln

( 1) c

G

n c

20 020

4ln

( 1)c cc

G

n c

2 202

2( )

( 1)c c

G

n c

24/9/2010 12

GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)

= 4GM / (c2 x)

x

y = y0 + K (x02 – x2), with K = 1/(2 Rsc)

y

dy/dx = -tg(r) with i + r + = π, i = r, and thus r = π/2 - /2and finally,

r i

24/9/2010 13

GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)

24/9/2010 14

GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)

24/9/2010 15

= 4GM / (c2 x)

x

y = y0 + K ln(x0 / x) with K = Rsc)

y

GL mirage simulator for the case of normal incidence light reflection

(point- like mass lens)

dy/dx = -r with i + r = , i = r, and thus r = /2and finally,

24/9/2010 16

GL mirage simulator for the case of normal incidence light reflection

(point- like mass lens)

24/9/2010 17

GL mirage simulator for the case of normal incidence light reflection

(point- like mass lens)

24/9/2010 18

GL mirage simulator for the case of grazing incidence light reflection (uniform disk lens)

y = y0 + K ln(x0 / x), with K = c2/(2GπΣ0)

24/9/2010 19

GL mirage simulator for the case of normal incidence light reflection (uniform disk lens)

y = y0 + K (x02 – x2) with K = (4G/c2)πΣ0

24/9/2010 20

The Optical GL Experiment (light relection)

24/9/2010 21

THE OPTICAL GL EXPERIMENT:

24/9/2010 22

THE OPTICAL GL EXPERIMENT:

24/9/2010 23

THE OPTICAL GL EXPERIMENT: