A new method for tracing rays through graded-index media is presented. The method essentially consists of transforming the ray equation into a convenient form and solving the resulting equation using a standard numerical technique. A detailed comparison of this method with existing methods has also been made, and it is shown that for obtaining a desired accuracy this method requires much less computational effort.

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Magnetic luminescent hybrid nanostructures (MLHN) have received a great deal of attention due to their potential biomedical applications such as thermal therapy, magnetic resonance imaging, drug delivery and intracellular imaging. We report the development of bifunctional Fe3O4 decorated YPO4:Eu hybrid nanostructures by covalent bridging of carboxyl PEGylated Fe3O4 and amine functionalized YPO4:Eu particles. The surface functionalization of individual nanoparticulates as well as their successful conjugation was evident from Fourier transform infrared (FTIR) spectroscopy, dynamic light scattering (DLS), zeta-potential and transmission electron microscopy (TEM) studies. X-ray diffraction (XRD) analysis reveals the formation of highly crystalline hybrid nanostructures. TEM micrographs clearly show the binding/anchoring of 10 nm Fe3O4 nanoparticles onto the surface of 100-150 nm rice grain shaped YPO4:Eu nanostructures. These MLHN show good colloidal stability, magnetic field responsivity and self-heating capacity under an external AC magnetic field. The induction heating studies confirmed localized heating of MLHN under an AC magnetic field with a high specific absorption rate. Photoluminescence spectroscopy and fluorescence microscopy results show optical imaging capability of MLHN. Furthermore, successful internalization of these MLHN in the cells and their cellular imaging ability are confirmed from confocal microscopy imaging. Specifically, the hybrid nanostructure provides an excellent platform to integrate luminescent and magnetic materials into one single entity that can be used as a potential tool for hyperthermia treatment of cancer and cellular imaging.