Refraction at a Spherical Surface

n If u be the distance of a point source, v the distance of the point image or the intersection of the refracted ray with the axis, n ₁ and n ₂ the indices of refraction of the first and second medium, and r the radius of curvature of the separating surface,

$${{n_2 } \over v} + {{n_1 } \over u} = {{n_2 - n_1 } \over r}$$

In the first medium is air the equation becomes,

$${n \over v} + {1 \over u} = {{n - 1} \over r}$$