to attain a fast or bright lens system having a better performance it is necessary to also satisfy the following conditions 5 6 7 8 9 and 10 with respect to the rear lens group also while the conditions 5 6 7 8 9 and 10 partially overlap the conditions set forth in the aforementioned u s application ser no 794 589 unless all the conditions of the present invention are simultaneously satisfied it is impossible to obtain the lens system to which the present invention is directed the condition 5 is effective to compensate for the distortion in the most wide angle zoom range in the positive direction the first lens of the rear lens group is positioned at the middle portion of the lens system in the most wide angle range the distortion aberration is critically determined by the selection of the position of the diaphragm however in order to prevent coma flare in the most wide angle range from being generated in the surfaces facing the image of the rear lens group and in order to position the diaphragm relatively near to the image plane in the surface facing the image of the first lens of the rear lens group it is effective to compensate for the distortion aberration in the most wide angle range in the positive direction the condition 5 is required to effectively compensate the effect described above that is exceeding the maximum limited.