Bi-convex vs. plano-convex lenses As I understand, less spherical aberration is obtained when a collimated beam is focused with a plano-convex lens as opposed to a biconvex lens. What would be a situation when a bi-convex lens should be used? When should one use a bi-convex lens vs a plano-convex lens?
 A: To elaborate on George's answer, a plano-convex lens is typically used in a telescope where both the beam coming in and the beam going out are collimated.  If the lenses are oriented correctly this will produce less aberration than a bi-convex lens.  In this case the correct orientation is to have the curved surfaces of the lens pointing out towards the collimated beams.  Note that if the lenses are oriented the other way, then this arrangement will produce more spherical aberration than the bi-convex case.  
To answer your question specifically, the bi-convex lens is the best lens to use in the situation where the beam incident on the lens is diverging and the beam leaving the lens is converging symmetrically.  I.E. the incident and outgoing beams are mirror images of each other.  
The idea to minimize spherical aberration when using spherical lenses is to trade-off between the two surfaces of the lens so that you show the beam the least curved surface, relative to the beams own curvature, at each refraction.  
There is actually a whole class of lenses known as 'best form' lenses (see e.g. this page of CVI's website) which perform better in telescopes with collimated beams than even plan-convex lenses.  Indeed, if you are willing to spend the money, you can do away with spherical aberration all together by using parabolic surfaces.  Typically you can only get parabolic mirrors, however, not lenses.  In an application requiring very fast telescopes, this is the way to go.  
A: As a general rule, the arrangement that more closely equalizes the deviation at the two surfaces, will yield the smallest spherical aberration.   That arrangement, minimizes the incidence angles and deviation at the two faces, and smaller incidence angles give less spherical aberration.
So an equi bi-convex lens would work better in a 1:! relay situation.   The plano-convex will work better at infinity focus.
