$$\require{cancel}$$
Figure II.12 shows a refracting interface of radius of curvature $$r$$ separating media of indices $$n_1$$ and $$n_2$$.
I show a real object at O, a real image at I and the centre of curvature at C. Remember that angles are small and the “lens” is thin. We see that $$h = \alpha p= \beta q = \gamma r$$. By Euclid, $$\theta_1 = \alpha + \gamma$$ and $$\theta_2 = \gamma - \beta$$, and by Snell, $$n_1\theta_1 = n_2\theta_2$$. From these we obtain
$\frac{n2}{q} = -\frac{n_1}{p} + \frac{n_2-n_1}{r}. \label{eq:2.8.3}$
Thus the power is $$\frac{n_2-n_1}{r}$$. The reader should try this for other situations (virtual object, virtual image, concave interface, and so on) to see that you always get the same result.