2. Gradient Refractive Index Gradient Refractive Index The refractive index of a particular point of a lens with a gradient refractive index The refractive index of a particular point of in a lens with a radial gradient refractive index The effects of gravitational potential as related to the effects of a refractive index G.R.I.N. LENS

3. 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) Angle of deflection: One ray. One Mass. Surface density must exceed critical mass density somewhere within the gravitational lens. For multiple images, the object must lie within the cusp.

4. 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)

5. Angular Deflection

6. Density Perturbations, Image to source mapping, Time delay R (Image)  S (Source) Time delay calculation is composed of the geometrical delay and the potential time delay

7. References Blandford, R., et al. Gravitational Lens Optics..JSTOR. Science. 245: 824-830. 1989. Web. Nov. 2010. 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. 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. 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. Mellier, Y., et al. Lecture Notes in Physics: Gravitational lensing. Berlin: Springer-Verlag, 1990.

8. Images King, L. U. Manchester. NICMOS,HST, NASA. 1998. http://apod.nasa.gov/apod/ap980330.html King, L. U. Manchester. NICMOS,HST, NASA. 1998. http://apod.nasa.gov/apod/ap980330.html 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 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 Solar Eclipses Overview. 2010. http://scie.eja.int/science_e/www/object/index.cfm?fobjectid= 37889&fbodylongid=1786 http://scie.eja.int/science_e/www/object/index.cfm?fobjectid= 37889&fbodylongid=1786 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 Grin Micro Lens. http://www.acphotonics.com/products/product_files/GRIN% 20/Lens.htm http://www.acphotonics.com/products/product_files/GRIN% 20/Lens.htm http://www.acphotonics.com/products/product_files/GRIN% 20/Lens.htm Optica Software. http://www.opticasoftware.com/faqs/ Optica Software. http://www.opticasoftware.com/faqs/http://www.opticasoftware.com/faqs/