Exhaustive study of reflection and refraction at spherical surfaces on the basis of the newly discovered generalized vectorial laws of reflection and refraction

This paper deals with the application of the newly discovered generalized vectorial laws of reflection and refraction for making an extensive analysis of reflection and refraction at spherical surfaces. Various cases of image formation have been considered. It has been observed that, direct application of the generalized vectorial laws of reflection and refraction leads to the appropriate formula of ray optics for each of the cases considered. The analysis of the results are ultimately summed up to give birth to the generalized mirror formula as well as the generalized formula for refraction at spherical surfaces. Also by using the results obtained for refraction at spherical surfaces, the Lens makers’ formulae have been finally offered.