= Solution
In the <paraxial approximation>, apply <refraction> at each surface of the <thin lens> in air. With signed radii $R_1$ and $R_2$, the first surface obeys $n/v_1-1/u=(n-1)/R_1$, and the second obeys $1/v-n/v_1=(1-n)/R_2$. The separation of the surfaces is neglected, so the intermediate image coordinate $v_1$ cancels:
$$
\frac1v-\frac1u=(n-1)\left(\frac1{R_1}-\frac1{R_2}\right)=\frac1f.
$$
This is <Lensmaker's equation>, with <Cartesian coordinate system> object coordinate $u<0$ for a real object. For an equiconvex <thin lens> and light travelling left to right, $R_1=R$ and $R_2=-R$. Hence
$$
\boxed{\frac1f=\frac{2(n-1)}R,\qquad f=\frac{R}{2(n-1)}.}
$$
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