Past exam of the physics 2 paper of the University of Oxford / 2019 / 7 / a / 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: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