Images formed by refraction:

The paraxial ray PA refracts and becomes AP'. All the related angles are small; then their sin is equal to their measure radian. The Snell's law is then written as: n1 i = n2 r

We have:
φ + β = i
β = r + α

n1 (φ + β ) = n2 (β - α)
(n2 - n1) β = n1 φ + n2 α

φ = AV/s
α = AV/s'
β = AV/R

(n2 - n1)/R = n1/s + n2/s'

                (n2 - n1)/R = n1/s + n2/s'