Question

Consider a thin lens placed between a source (S) and an observer (O) (Fig.). Let the thickness of the lens vary as `w(b)=w_0-b^2/a`, where b is the verticle distance from the pole. w₀ is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.