Transcript Gravitation Lensing

Gradient Refractive Index
The refractive index of a particular point of in a
lens with a radial gradient refractive index
The refractive index of a particular point of a
with of
a gradient
refractive
index
Thelens
effects
gravitational
potential
as related to the
effects of a refractive index
G.R.I.N. LENS
Angle of deflection: One ray. One Mass.
In reality we have multiple masses… Vector superposition!
“The total deflection angle is the vector superposition of the deflections
due to all the mass elements of the lens.” (Blandford et al. 825)
Surface density must exceed critical mass density somewhere
within the gravitational lens.
For multiple images, the object must lie within the cusp.
Ray Tracing: Multiple images
Caustic cusp due to the
gravitational lens is shown in ray
tracing using the angle of deflection
for individual rays in superposition.
Einstein Ring
First complete ring
observed
Hubble Telescope (1998)
Angular Deflection
Density Perturbations, Image to
source mapping, Time delay
Time delay calculation is
composed of the
geometrical delay and the
potential time delay
R (Image)  S (Source)
References
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Blandford, R., et al. Gravitational Lens Optics. .JSTOR.
Science. 245: 824-830. 1989. Web. Nov. 2010.
Bradac, M., et al. Revealing The Properties of Dark Matter
in the Merging Cluster Macs J0025.4-1222.
arXiv:0806.2320v2 [astro-ph]. 2008. Web. Nov. 2010.
Levine, H., A. Petters, J.Wambsganss. Singularity Theory
and Gravitational Lensing. Boston: Birkhauser, 2001.
Mellier, Y., et al. Lecture Notes in Physics: Gravitational
lensing. Berlin: Springer-Verlag, 1990.
Images
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King, L. U. Manchester. NICMOS ,HST, NASA. 1998.
http://apod.nasa.gov/apod/ap980330.html
Tsioulia, Andrew,. Gradient Index (GRIN) Lens. 2003
http://www.informaworld.com/smpp/contentncontent=a71354
8186~db=all~dumptype=rss
Solar Eclipses Overview. 2010.
http://scie.eja.int/science_e/www/object/index.cfm?fobjectid=
37889&fbodylongid=1786
Grin Micro Lens.
http://www.acphotonics.com/products/product_files/GRIN%
20/Lens.htm
Optica Software. http://www.opticasoftware.com/faqs/