NOVELTY - A composition (C1) for increasing the transmission of light between two mediums having different indices of refraction, where the composition is disposed between the two mediums and the light is transmitted through the composition, comprises a matrix having a first index of refraction, and scattering particles having a second index of refraction not equal to the first index of refraction, where the scattering particles are dispersed in the matrix and scatter a portion of the light transmitted through the composition to thereby increase the transmission of light between the two mediums.    USE - As composition for increasing the transmission of light between two mediums having different indices of refraction; for forming transitional layer used to increase transmission of light between two medium having different indices of refraction (claimed), where the transitional layer separates two fluids (i.e. liquid or gas) and can be used in devices, e.g. such as LED's and OLED's, cold mirrors for telescopes, anti-bird-collision coatings for architectural glass, 'low-e' coatings for glass, televisions, solar cells, light fixtures, mobile devices such as cell phone glass, structural glass, automotive and other transportation glass, etc..    ADVANTAGE - The composition forms transitional layer that increases the transmission or reflection of light between two mediums having different indices of refraction. The composition is inexpensive and uses non-poisonous starting materials that are not air sensitive, reduces the cost of the deposition and increases the size of the substrate that can be treated. The composition provides increase in the transmission or reflectance of light between two materials having different indices of refraction. The transitional layer reduces the reflection loss at an interface of the two materials due to the bridging the difference in the indices of refraction between the two mediums. The transitional layer reduces the reflection loss at such interface. The transitional layer can increase the reflection between the two mediums. The methods of forming have the benefit of simple and efficient execution, are able to be used in a number of diverse applications, and can be tailored for application over large substrate areas. The methods of forming also provide for application and firing of the pastes to be accomplished at atmospheric conditions. The use of vacuum equipment and other expensive procedures is thus eliminated.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a method (M1) of forming a transitional layer used to increase the transmission of light between two mediums having different indices of refraction, where the transitional layer is disposed between the two mediums and the light is transmitted through the transition layer, where the method involves: disposing a composition between the two mediums; and processing the composition to form the transitional layer comprising scattering particles having a first index of refraction dispersed in a matrix having a second index of refraction not equal to the first index of refraction, where a portion of the light transmitted through the transitional layer is scattered by the scattering particles to thereby increase the transmission of light between the two mediums;    (2) a method (M2) for increasing the transmission of light between two mediums having different indices of refraction involving: providing a transitional layer comprising scattering particles having a first index of refraction dispersed in a matrix having a second index of refraction not equal to the first index of refraction; positioning the transitional layer between the two mediums; and transmitting the light through the transitional layer, where the scattering particles scatter a portion of the light transmitted through the transitional layer to thereby increase the transmission of light between the two mediums;    (3) a composition (C2) for increasing the transmission of light between a first medium having a first index of refraction and a second medium having a second index of refraction that is different from the first index of refraction, where the composition is disposed between the first medium and the second medium and the transmission of light is increased by transmitting the light through a thickness of the composition, where the composition comprises: a single layer comprising transparent metal-oxides, where the layer has a gradient index of refraction through a thickness of the layer from a portion of the layer closest to the first medium to a portion of the layer closest to the second medium;    (4) a method (M3) of forming a transitional layer used to increase the transmission of light between a first medium having a first index of refraction and a second medium having a second index of refraction that is different from the first index of refraction, where the transitional layer is a single layer and is disposed between the first medium and the second medium and the transmission of light is increased by transmitting the light through a thickness of the transitional layer, when the method involves: disposing a composition between the first medium and second medium; and processing the composition to form the transitional layer comprising transparent metal-oxides that produce a gradient index of refraction through a thickness of the transitional layer from a portion of the transitional layer closest to the first medium to a portion of the transitional layer closest to the second medium;    (5) a method (M4) of forming a transparent light extracting transitional layer with selectable index of refraction on a substrate involving: providing a substrate, a soluble metal complex, a complex-forming agent, a resin, and a solvent capable of dissolving the soluble metal complex and the resin; dissolving the soluble metal complex, the one complex-forming agent, and the resin in the solvent to form a metal oxide precursor paste; depositing the metal oxide precursor paste on the substrate; and heating the metal oxide precursor paste to a temperature and for a duration to burn off the solvent and the resin and oxidize the soluble metal complex, to form a transparent transitional layer of metal oxide on the substrate, where the transitional layer has an index of refraction between that of the substrate and that of air;    (6) a method (M5) of forming transparent light extracting layers with selectable indices of refraction on a substrate; and    (7) a method (M6) of forming light reflecting layers with selectable indices of refraction on substrate.