2. 24/9/20101 Le Petit Prince (Antoine de St Exupéry) 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)

3. 24/9/20102 (A): Gravitational lensing(B): Optical lens experiment Deflector plane Observer plane Lens plane O1O1 O1O1 O2O2 O2O2

4. 24/9/20103 (A): Gravitational lensing(B): Optical lens experiment Deflector plane Observer plane Lens plane O1O1 O1O1 O2O2 O2O2  

5. 24/9/20104 (A): Gravitational lensing(B): Optical lens experiment Deflector plane Observer plane Lens plane O1O1 O1O1 O2O2 O2O2     

6. 24/9/20105  r n i ε(ξ)ε(ξ) 

7. 6 2. Gravitational lenses 5. 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.

8. 24/9/20107 2. Gravitational lenses 5. THE OPTICAL GL EXPERIMENT: 5.1. Shapes of axially symmetric optical lenses:, (5.1), (5.2), (5.3), (5.4). (5.5)

9. 24/9/20108 2. Gravitational lenses 5. 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 lenses simulating 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).

10. 24/9/20109 2. Gravitational lenses 5. 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)

11. 24/9/201010 2. Gravitational lenses 5. THE OPTICAL GL EXPERIMENT: 5.1. Shapes of axially symmetric optical lenses:, (5.11) M(  ) =   0  2, if    c, (5.12a) M(  ) =   0  c 2, if    c. (5.12b)

12. 24/9/201011 2. Gravitational lenses 5. THE OPTICAL GL EXPERIMENT: 5.1. Shapes of axially symmetric optical lenses: if  c     0, (5.13a) (5.13b) if    c. (5.13c)

13. 24/9/201012 GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)  = 4GM / (c 2 x)  x y = y 0 + K (x 0 2 – x 2 ), with K = 1/(2 R sc ) y dy/dx = -tg(r) with i + r +  = π, i = r,and thus dy/dx = -tg(r) with i + r +  = π, i = r, and thus r = π/2 -  /2 and finally, r i

14. 24/9/201013 GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)

15. 24/9/201014 GL mirage simulator for the case of grazing incidence light reflection (point-like mass lens)

16. 24/9/201015  = 4GM / (c 2 x)  x y = y 0 + K ln(x 0 / 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 dy/dx = -r with i + r = , i = r, and thus r =  /2 and finally,

17. 24/9/201016 GL mirage simulator for the case of normal incidence light reflection (point- like mass lens)

18. 24/9/201017 GL mirage simulator for the case of normal incidence light reflection (point- like mass lens)

19. 24/9/201018 GL mirage simulator for the case of grazing incidence light reflection (uniform disk lens) y = y 0 + K ln(x 0 / x), with K = c 2 /(2GπΣ 0 )

20. 24/9/201019 GL mirage simulator for the case of normal incidence light reflection (uniform disk lens) y = y 0 + K (x 0 2 – x 2 ) with K = (4G/c 2 )πΣ 0

21. 24/9/201020 The Optical GL Experiment (light relection)

22. 24/9/201021 THE OPTICAL GL EXPERIMENT:

23. 24/9/201022 THE OPTICAL GL EXPERIMENT:

24. 24/9/201023 THE OPTICAL GL EXPERIMENT: