Gradient Refractive Index The refractive index of a

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Gradient Refractive Index The refractive index of a particular point of in a lens

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 lens a gradient refractivepotential index as related to the Thewith effects of gravitational effects of a refractive index G. R. I. N. LENS

Angle of deflection: One ray. One Mass. In reality we have multiple masses… Vector

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: 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

Angular Deflection

Density Perturbations, Image to source mapping, Time delay calculation is composed of the geometrical

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

References n n Blandford, R. , et al. Gravitational Lens Optics. . JSTOR. Science.

References n n 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 J 0025. 4 -1222. ar. Xiv: 0806. 2320 v 2 [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 n n n King, L. U. Manchester. NICMOS , HST, NASA. 1998. http:

Images n n n King, L. U. Manchester. NICMOS , HST, NASA. 1998. http: //apod. nasa. gov/apod/ap 980330. html Tsioulia, Andrew, . Gradient Index (GRIN) Lens. 2003 http: //www. informaworld. com/smpp/contentncontent=a 71354 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%2 0/Lens. htm Optica Software. http: //www. opticasoftware. com/faqs/

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REFRACTIVE SURGERY Refractive surgical techniques have evolved rapidlyREFRACTIVE SURGERY Refractive surgical techniques have evolved rapidly
REFRACTIVE ERRORS Definition Refractive errors occurs when theREFRACTIVE ERRORS Definition Refractive errors occurs when the
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