why is the focal length of a convex lens is taken positive and that of a concave lens as negative?
In a convex lens , since the parallel beam of light travelling parallel to the principal axis actually meets at a point(second focus) , the focus is called real focus and its focal length is taken as positive.
In a concave lens , since the parallel beam of light travelling parallel to the principal axis appear to diverge from this point(second focus) , the focus is called virtual focus and its focal length is taken as negative.