be effectively reduced by satisfying the conditional formula a5 the present optical system having the small optical total length at the telephoto side despite having a zoom ratio of over 18 u00d7 contributes to achieving a compact lens barrel and a compact camera if simply the optical total length at the telephoto side is reduced it leads to total increase in the optical power of each of the lens groups which makes it difficult to correct aberration in contrast if the lateral magnification of the fourth lens group at the telephoto end is made comparatively small so as to satisfy the conditional formula a5 it is possible to reduce the optical total length if an upper limit of the conditional formula a5 is exceeded a combined focal length of the first to third lens groups becomes short which makes it difficult to correct aberration above all field curvature if a lower limit of the conditional formula a5 is fallen short of the optical total length increases which is not preferable from the viewpoint of achieving compactness furthermore if the lower limit of the conditional formula a5 is fallen short of need arises to increase the refractive power of the second lens group which may in turn increase astigmatism and need arises to increase the refractive power of the third lens group which may in turn increase spherical aberration it is preferable that the following conditional formula a6 be satisfied ywmax represents a maximum real image height.