hereinafter , taking optical systems embodying the present invention will be described with reference to the corresponding drawings . fig1 and 2 , fig3 and 4 , fig5 and 6 , fig7 and 8 , and fig9 and 10 show the lens arrangement of the taking optical systems of a first to a fifth embodiment , respectively , of the invention . the taking optical system of the first embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), is composed solely of a main optical system l 1 , as shown in fig1 . in this figure , the left - hand side is the object side and the right - hand side is the image side . the main optical system l 1 is built as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the first embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ) has a conversion optical system a 1 additionally disposed between the main optical system l 1 and the low - pass filter lpf , as shown in fig2 . the conversion optical system a 1 is composed of two lens elements g 12 and g 13 . the taking optical system of the second embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), is composed solely of a main optical system l 2 , as shown in fig3 . in this figure , the left - hand side is the object side and the right - hand side is the image side . the main optical system l 2 is built , like that of the first embodiment , as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the second embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ) has a conversion optical system a 2 additionally disposed between the main optical system l 2 and the low - pass filter lpf , as shown in fig4 . the conversion optical system a 2 is composed of two lens elements g 12 and g 13 . the taking optical system of the third embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), is composed solely of a main optical system l 3 , as shown in fig5 . in this figure , the left - hand side is the object side and the right - hand side is the image side . the main optical system l 3 is built , like that of the first embodiment , as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the third embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ) has a conversion optical system a 3 additionally disposed between the main optical system l 3 and the low - pass filter lpf , as shown in fig6 . the conversion optical system a 3 is composed of two lens elements g 12 and g 13 . the taking optical system of the fourth embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), is composed solely of a main optical system l 4 , as shown in fig7 . in this figure , the left - hand side is the object side and the right - hand side is the image side . the main optical system l 4 is built , like that of the first embodiment , as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the fourth embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ) has a conversion optical system a 4 additionally disposed between the main optical system l 4 and the low - pass filter lpf , as shown in fig8 . the conversion optical system a 4 is composed of two lens elements g 12 and g 13 . the taking optical system of the fifth embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 2 . 3 mm ), is composed solely of a main optical system l 5 , as shown in fig9 . in this figure , the left - hand side is the object side and the right - hand side is the image side . the main optical system l 5 is built , like that of the first embodiment , as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the fifth embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ) has a conversion optical system a 5 additionally disposed between the main optical system l 5 and the low - pass filter lpf , as shown in fig1 . the conversion optical system a 5 is composed of two lens elements g 12 and g 13 . in any of these embodiments , other things being equal , the taking optical system is larger when configured for the second frame - format than when configured for the first frame - format . therefore , in converting the frame - format , rearranging the configuration for the second frame - format into the configuration for the first frame - format by adding the conversion optical system to the former results in making the thus converted taking optical system unduly large for the first frame - format . accordingly , it is more advantageous in terms of miniaturization to rearrange the configuration for the first frame - format into the configuration for the second frame - format by adding the conversion optical system to the former , as is practiced in the embodiments described above . the conditions which are preferably fulfilled by these taking optical systems will be described below . in the embodiments 1 to 5 described above , it is preferable that the taking optical system , when configured for the second frame - format , fulfill condition ( 1 ) below . condition ( 1 ) defines the focal length of the conversion optical system . if the value of condition ( 1 ) is equal to or less than its lower limit , the focal length of the conversion optical system is so short , i . e . the optical power thereof is so strong , that it is difficult to correct aberrations , in particular barrel - shaped distortion and curvature of field . in contrast , if the value of condition ( 1 ) is equal to or greater than its upper limit , the focal length of the conversion optical system is so long , i . e . the optical power thereof is so weak , that it is difficult to obtain sufficiently high magnification . as a result , it is not possible to obtain a significant difference between the focal lengths observed without and with the conversion optical system , and thus the taking optical system , when configured for the second frame - format , is so wide - angle oriented that it is difficult to correct peripheral imaging performance , in particular curvature of field . in the embodiments 1 to 5 , it is preferable that the taking optical system , when configured for the second frame - format , fulfill condition ( 2 ) below . condition ( 2 ) defines the magnification of the conversion optical system . if the value of condition ( 2 ) is equal to or less than its lower limit , the conversion magnification is so low that the focal length of the taking optical system is not enlarged sufficiently even when the conversion optical system is added thereto , and thus the taking optical system is so wide - angle oriented that it is difficult to correct curvature of field . in contrast , if the value of condition ( 2 ) is equal to or greater than its upper limit , the conversion magnification is so high that it is difficult to correct aberrations , in particular barrel - shaped distortion and curvature of field . in the embodiments 1 to 5 , it is preferable that the taking optical system fulfill condition ( 3 ) below . condition ( 3 ) defines the relationship between the ratio of the second frame - format to the first frame - format and the conversion magnification , and thus defines the condition to be fulfilled to obtain roughly equal angles of view without and with the conversion optical system . if the value of condition ( 3 ) is out of the range defined above , the difference between the angles of view without and with the conversion optical system is unduly great , increasing the burden on the main optical system , which is used in both the configurations for the first and second frame - formats , in terms of handling of different angles of view . this inconveniently leads to an increase in the total length of the entire taking optical system , to an increase in the diameter of the front - end lens unit , and to an increase in the number of lens elements needed to compensate for aggravated aberrations . specifically , if the value of condition ( 3 ) is equal to or less than its lower limit , the focal length range with the conversion optical system is shifted excessively toward the telephoto side , and thus the entire lens system needs to have an unduly long total length ; in addition , unduly large spherical aberration appears . in contrast , if the value of condition ( 3 ) is equal to or greater than its upper limit , the focal length range with the conversion optical system is shifted excessively toward the wide - angle side , and thus the front - end lens unit needs to have an unduly large diameter ; in addition , unduly large curvature of field and distortion appear . in the embodiments 1 to 5 , it is preferable that the taking optical system , when configured for the first frame - format , fulfill condition ( 4 ) below . f 2 represents the focal length of the second lens unit ; and fws represents the focal length of the entire taking optical system , when configured for the first frame - format , as observed at the wide - angle end . if the value of condition ( 4 ) is equal to or less than its lower limit , the focal length of the second lens unit is too short , i . e . the optical power thereof is too strong , and thus , irrespective of whether the taking optical system is configured for the first frame - format or for the second frame - format with the conversion optical system added thereto , it is difficult to correct the negative distortion occurring at the wide - angle end , and in addition curvature of field exhibits an unduly strong inclination toward the under side . in contrast , if the value of condition ( 4 ) is equal to or greater than its upper limit , the second lens unit needs to be moved through so long a distance for zooming that the front - end lens unit needs to have an unduly large diameter . note that , although the embodiments described above deal only with cases where frame - format conversion is achieved in a taking optical system by adding a conversion optical system thereto with the configuration of the main optical system left untouched , it is also possible , for example , to modify part of the configuration of the main optical system without changing its principal characteristics , and then add a conversion optical system thereto . example of methods that allow the principal characteristics of the main optical system to be left untouched include so - called bending , whereby the radius of curvature of the single lens element constituting the main optical system is changed without changing its optical power , and addition of an aspherical surface or a diffractive optical surface . also categorized into methods that allow the principal characteristics of the main optical system to be left untouched is addition thereto of a spherical lens , cemented lens , aspherical lens , diffractive optical lens , or the like having , in any case , a weak power for the purpose of improving image plane characteristics . modifying part of the configuration of the main optical system as described above is effective in improving optical performance particularly in the configuration for the larger frame - format . because the configuration for the larger frame - format is used with an image sensing device having a larger number of pixels , and is accordingly required to offer higher optical performance than that for the smaller frame - format . moreover , although the embodiments described above deal only with cases where the main optical system and the conversion optical system are both composed solely of refractive surfaces , it is also possible to adopt , depending on the requirements imposed by the image taking apparatus into which the taking optical system is incorporated , an arrangement having a mirror disposed in the optical path so as to turn the optical path , or an arrangement including a diffractive optical element . moreover , although the embodiments described above provide only examples of taking optical systems for use with image sensing devices having different frame - formats , the techniques underlying them are applicable also to taking optical systems designed for use with both an image sensing device having a smaller frame - format and a silver - halide film having a larger frame - format , or to taking optical systems designed for use with both conventional 35 mm silver - halide film and new - generation silver - halide film ( i . e . aps film used in the advanced photo system ). fig2 and 22 , fig2 and 24 , and fig2 and 26 show the lens arrangement of the taking optical systems of a sixth to an eighth embodiment , respectively , of the invention . note that , in each diagram , arrows schematically indicate the movement of the lens units , which will be described later , during zooming from the wide - angle end to the telephoto end . arrows with a broken line indicate that the lens unit is kept in a fixed position during zooming . moreover , each diagram shows the lens arrangement of the taking optical system during zooming , as observed at the wide - angle end . the taking optical system of the sixth embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), has the construction as shown in fig2 . in this figure , the left - hand side is the object side and the right - hand side is the image side . this lens system is built as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . here , the first lens unit gr 1 is referred to as the “ first object - side lens unit ”. gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the sixth embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ), has a construction as shown in fig2 , and is thus constructed basically in the same manner as in fig2 except that , in the former , the first lens unit is replaced with another one in the zoom range between the middle - focal - length position and the telephoto end described later . here , the first lens units is referred to as the “ second object - side lens unit ”. the other lens units placed behind the first lens unit in fig2 and 22 have the same construction and are moved in the same way during zooming . the taking optical system of the seventh embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), has the construction as shown in fig2 . in this figure , the left - hand side is the object side and the right - hand side is the image side . this lens system is built as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 1 and gr 3 are stationary and gr 2 and gr 4 are movable . here , the first lens unit gr 1 is referred to as the “ first object - side lens unit ”. gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the seventh embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ), has a construction as shown in fig2 , and is thus constructed basically in the same manner as in fig2 except that , in the former , the first lens unit is replaced with another one in the zoom range between the middle - focal - length position and the telephoto end described later . here , the first lens unit is referred to as the “ second object - side lens unit ”. the other lens units placed behind the first lens unit in fig2 and 24 have the same construction and are moved in the same way during zooming . the taking optical system of the eighth embodiment , when configured for a first frame - format ( a smaller frame - format , of which the height y in a direction perpendicular to the optical axis = 3 . 1 mm ), has the construction as shown in fig2 . in this figure , the left - hand side is the object side and the right - hand side is the image side . this lens system is built as a four - unit zoom lens system of a positive - negative - positive - positive configuration composed of , from the object side , a first lens unit gr 1 , a second lens unit gr 2 , a third lens unit gr 3 , and a fourth lens unit gr 4 , of which gr 3 is stationary and gr 1 , gr 2 , and gr 4 are movable . here , the first lens unit gr 1 is referred to as the “ first object - side lens unit ”. gr 1 consists of three lens elements g 1 , g 2 , and g 3 ; gr 2 consists of three lens elements g 4 , g 5 , and g 6 ; gr 3 consists of two lens elements g 7 and g 8 and an aperture stop s ; and gr 4 consists of three lens elements g 9 , g 10 , and g 11 . in addition , a low - pass filter lpf shaped like a flat plate is disposed at the image - side end of the taking optical system . on the other hand , the taking optical system of the eighth embodiment , when configured for a second frame - format ( a larger frame - format , of which the height y in a direction perpendicular to the optical axis = 4 . 0 mm ), has a construction as shown in fig2 , and is thus constructed basically in the same manner as in fig2 except that , in the former , the first lens unit is replaced with another one in the zoom range between the middle - focal - length position and the telephoto end described later . here , the first lens unit is referred to as the “ second object - side lens unit ”. the other lens units placed behind the first lens unit in fig2 and 26 have the same construction and are moved in the same way during zooming in any of these embodiments , other things being equal , the taking optical system is larger when configured for the second frame - format than when configured for the first frame - format . therefore , exchanging the first lens unit yields no advantage , because , as explained earlier in the description of the prior art , the size of the entire taking optical system is determined by its size when configured for the larger frame - format . incidentally , in zoom - type taking optical systems , like those of the embodiments of the present invention , during zooming from the wide - angle end to the telephoto end , the lens units are moved in such a way that the distance between the first and second lens units increases and that the distance between the second lens unit and the lens units placed behind it , including the aperture stop , decreases . in general , the diameter of such a zoom - type taking optical system as a whole depends on the diameter of the front - end lens unit thereof . here , by adopting an arrangement that can be adapted to the second frame - format by exchanging the first lens unit in the zoom range between the middle - focal - length position and the telephoto end of the configuration for the first frame - format , it is possible to reduce the increased distance between the first and second lens units and thereby place the first lens unit closer to the second lens unit , and as a result , now that the distance between the second lens unit and the lens units placed behind it , including the aperture stop , is reduced , it is possible to position the entrance pupil closer . this helps achieve a considerable reduction in the diameter of the front - end lens unit . what is important here is that , in order for the second lens unit to offer the same zoom solution irrespective of whether the first lens unit is exchanged or not , the second lens unit needs to offer substantially the same magnification . that is , in either case , the image point position of the first lens unit ( the second object - side lens unit ) with respect to the second lens unit as observed in the zoom range between the wide - angle end and the telephoto end when the taking optical system is configured for the second frame - format needs to coincide with the image point position of the first lens unit ( the first object - side lens unit ) with respect to the second lens unit as observed in the zoom range between the middle - focal - length position and the telephoto end when configured for the first frame - format . as described above , by adopting an arrangement that can be adapted to the second frame - format by exchanging the first lens unit in the zoom range between the middle - focal - length position and the telephoto end of the configuration for the first frame - format , it is possible to realize a taking optical system that can cope with both the first frame - format and the second frame - format without sacrificing its size when configured for the first frame - format . moreover , this permits the zoom solution of the lens units disposed behind the first lens unit to remain invariable , and thus contributes greatly to the standardization of the structures of lens barrels . the conditions which are preferably fulfilled by the taking optical systems will be described below . in the embodiments 6 to 8 described above , it is preferable that the taking optical system fulfill condition ( 5 ) below . f 1 s represents the focal length of the first object - side lens unit ; and f 1 b represents the focal length of the second object - side lens unit . condition ( 5 ) defines the ratio of the focal length of the second object - side lens unit to that of the first object - side lens unit , and thus defines the condition to be fulfilled to achieve proper aberration correction and to set the above - described image point of the first lens unit in an appropriate position . if the value of condition ( 5 ) is equal to or less than its lower limit , the focal length of the second object - side lens unit is too short relative to that of the first object - side lens unit , and thus it is difficult to obtain satisfactory peripheral imaging performance at the wide - angle end , and it is difficult to secure a sufficient distance between the first and second lens units at the wide - angle end to set the image point of the first lens unit in an appropriate position . in contrast , if the value of condition ( 5 ) is equal to or greater than its upper limit , the focal length of the second object - side lens unit is too long relative to that of the first object - side lens unit , and thus the distance between the first and second lens units is unduly long at the wide - angle end . this inconveniently leads to an increase in the total length of the entire taking optical system and to an increase in the diameter of the front - end lens unit . in the embodiments 6 to 8 , it is preferable that the taking optical system fulfill condition ( 6 ) below . zb represents the zoom ratio of the taking optical system , when configured for the second frame - format ; and zs represents the zoom ratio of the taking optical system , when configured for the first frame - format . if the value of condition ( 6 ) is equal to or less than its lower limit , the zoom ratio of the taking optical system , when configured for the second frame - format , is too low , and thus it is impossible to gain an appreciable advantage by exchanging the first lens unit . in contrast , if the value of condition ( 6 ) is equal to or greater than its upper limit , the zoom ratio of the taking optical system , when configured for the second frame - format , is too high , and thus , as described previously , the taking optical system is unduly large relative to the first frame - format . in the embodiments 6 to 8 , it is preferable that the taking optical system , when configured for the first frame - format , fulfill condition ( 7 ) below . f 2 represents the focal length of the second lens unit ; and fws represents the focal length of the entire taking optical system , when configured for the first frame - format , as observed at the wide - angle end . if the value of condition ( 7 ) is equal to or less than its lower limit , the focal length of the second lens unit is too short , i . e . the optical power thereof is too strong , and thus , irrespective of whether the taking optical system is configured for the first frame - format or for the second frame - format with the first lens unit exchanged , it is difficult to correct the negative distortion occurring at the wide - angle end , and in addition curvature of field exhibits an unduly strong inclination toward the under side . in contrast , if the value of condition ( 7 ) is equal to or greater than its upper limit , the second lens unit needs to be moved through so long a distance for zooming that the front - end lens unit needs to have an unduly large diameter . in the embodiments 6 to 8 , it is preferable that the taking optical system fulfill condition ( 8 ) below . condition ( 8 ) defines the conversion magnification of the frame - format . if the value of condition ( 8 ) is equal to or less than its lower limit , the ratio between the two frame - formats is so high that the total length of the taking optical system is unduly long . in contrast , if the value of condition ( 8 ) is equal to or greater than its upper limit , the ratio between the frame - formats is so low that exchanging the first lens unit yields no appreciable advantage . note that , although the embodiments described above deal only with cases where frame - format conversion is achieved in a taking optical system by exchanging the first lens unit thereof with the configuration of the lens units placed behind it left untouched , it is also possible , for example , to modify part of the configuration of the lens units placed behind the first lens unit without changing their principal characteristics , and then exchange the first lens unit . example of methods that allow the principal characteristics of the lens units placed behind the first lens unit to be left untouched include so - called bending , whereby the radii of curvature of the single lens elements constituting the lens units placed behind the first lens unit are changed without changing their optical powers , and addition of an aspherical surface or a diffractive optical surface . also categorized into methods that allow the principal characteristics of the lens units placed behind the first lens unit to be left untouched is addition thereto of a spherical lens , cemented lens , aspherical lens , diffractive optical lens , or the like having , in any case , a weak power for the purpose of improving image plane characteristics . modifying part of the configuration of the lens units placed behind the first lens unit as described above is effective in improving optical performance particularly in the configuration for the larger frame - format . because the configuration for the larger frame - format is used with an image sensing device having a larger number of pixels , and is accordingly required to offer higher optical performance than that for the smaller frame - format . moreover , although the embodiments described above deal only with cases where the taking optical system is composed solely of refractive surfaces , it is also possible to adopt , depending on the requirements imposed by the image taking apparatus into which the taking optical system is incorporated , an arrangement having a mirror disposed in the optical path so as to turn the optical path , or an arrangement including a diffractive optical element . moreover , although the embodiments described above provide only examples of taking optical systems for use with image sensing devices having different frame - formats , the techniques underlying them are applicable also to taking optical systems designed for use with both an image sensing device having a smaller frame - format and a silver - halide film having a larger frame - format , or to taking optical systems designed for use with both conventional 35 mm silver - halide film and new - generation silver - halide film ( i . e . aps film used in the advanced photo system ). hereinafter , examples of taking optical systems embodying the present invention will be presented with reference to their construction data , graphic representations of aberrations , and other data . examples 1 to 8 presented below correspond to the first to eighth embodiments , respectively , described above . tables 1 , 3 , 5 , 7 , 9 , 12 , 14 , and 16 list the construction data of examples 1 to 8 , respectively , when configured for the first frame - format , thus corresponding to the lens arrangements shown in fig1 , 5 , 7 , 9 , 21 , 23 , and 25 , respectively . tables 2 , 4 , 6 , 8 , 10 , 13 , 15 , and 17 list the construction data of examples 1 to 8 , respectively , when configured for the second frame - format , thus corresponding to the lens arrangements shown in fig2 , 6 , 8 , 10 , 22 , 24 , and 26 , respectively . in the construction data of these examples , ri ( i = 1 , 2 , 3 , . . . ) represents the ith surface counted from the object side and its radius of curvature , di ( i = 1 , 2 , 3 , . . . ) represents the ith axial distance counted from the object side , and ni ( i = 1 , 2 , 3 , . . . ) and vi ( i = 1 , 2 , 3 , . . . ) respectively represent the refractive index for the d line and the abbe number of the ith lens element counted from the object side . in the construction data of examples 1 to 5 , for each of the focal length f of the entire taking optical system , the f number fno of the entire taking optical system , the distance between the first and second lens units , the distance between the second and third lens units , the distance between the third and fourth lens units , and the distance between the last lens unit of the main optical system and the low - pass filter ( or the conversion optical system ), three values are given which are observed at , from left , the wide - angle end ( w ), the middle - focal - length position ( m ), and the telephoto end ( t ). in the construction data of examples 6 to 8 , for each of the focal length f of the entire taking optical system , the f number fno of the entire taking optical system , the distance between the first and second lens units , the distance between the second and third lens units , the distance between the third and fourth lens units , and the distance between the last lens unit of the taking optical system and the low - pass filter , three values are given which are observed at , from left , the wide - angle end ( w ), the middle - focal - length position ( m ), and the telephoto end ( t ). note that , in all of examples , a surface whose radius of curvature is marked with an asterisk (*) is an aspherical surface , whose surface shape is defined by the following formulae : x 0 = cy 2 /{ 1 +( 1 − εc 2 y 2 ) ½ } ( b ) y represents the height in a direction perpendicular to the optical axis ; fig1 a to 11 i , 13 a to 13 i , 15 a to 15 i , 17 a to 17 i , 19 a to 19 i , 27 a to 27 i , 29 a to 29 i , and 31 a to 31 i are graphic representations of the aberrations observed in the taking optical systems of examples 1 to 8 , respectively , when configured for the first frame - format ; and fig1 a to 12 i , 14 a to 14 i , 16 a to 16 i , 18 a to 18 i , 20 a to 20 i , 28 a to 28 i , 30 a to 30 i , and 32 a to 32 i are graphic representations of the aberrations observed in the taking optical systems of examples 1 to 8 , respectively , when configured for the second frame - format . of these diagrams , fig1 a to 11 c , 12 a to 12 c , 13 a to 13 c , 14 a to 14 c , 15 a to 15 c , 16 a to 16 c , 17 a to 17 c , 18 a to 18 c , 19 a to 19 c , 20 a to 20 c , 27 a to 27 c , 28 a to 28 c , 29 a to 29 c , 30 a to 30 c , 31 a to 31 c , and 32 a to 32 c show the aberrations observed at the wide - angle end [ w ]; fig1 d to 11 f , 12 d to 12 f , 13 d to 13 f , 14 d to 14 f , 15 d to 15 f , 16 d to 16 f , 17 d to 17 f , 18 d , to 18 f , 19 d to 19 f , 20 a to 20 f , 27 d to 27 f , 28 d to 28 f , 29 d to 29 f , 30 d to 30 f , 31 d to 31 f , and 32 d to 32 f show the aberrations observed at the middle focal length [ m ]; fig1 g to 11 i , 12 g to 12 i , 13 g to 13 i , 14 g to 14 i , 15 g to 15 i , 16 g to 16 i , 17 g to 17 i , 18 g to 18 i , 19 g to 19 i , 20 g to 20 i , 27 g to 27 i , 28 g to 28 i , 29 g to 29 i , 30 g to 30 i , 31 g to 31 i , and 32 g to 32 i show the aberrations observed at the telephoto end [ t ]. in the spherical aberration diagrams , the solid line ( d ) represents the spherical aberration observed for the d line and the broken line ( sc ) represents the sine condition . in the astigmatism diagrams , the solid line ( ds ) represents the astigmatism observed on the sagittal plane and the broken line ( dm ) represents the astigmatism observed on the meridional plane . examples 1 to 5 , when configured for the first or second frame - format , fulfill corresponding one or ones of conditions ( 1 ) to ( 4 ) described previously . examples 6 to 8 , when configured for the first or second frame - format , fulfill corresponding one or ones of conditions ( 5 ) to ( 8 ) described previously .