# Proceeding from Fermat's principle derive the refraction formula for paraxial rays on a spherical boundary surface

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Proceeding from Fermat's principle derive the refraction formula for paraxial rays on a spherical boundary surface of radius R between media with refractive indices n and n'.

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For O1 to be the image, the optical paths of all rays OAO1 must be equal upto terms of leading order in h Thus

n1OA + n2AO1 = constant