Patent Publication Number: US-2006017834-A1

Title: Imaging optical system and imaging lens device

Description:
This application is based on Japanese Patent Application Nos. 2004-216517, 2004-315771, 2005-38323, and 2005-41203 respectively filed on Jul. 23, 2004, Oct. 29, 2004, Feb. 15, 2005, and Feb. 17, 2005 the contents of which are hereby incorporated by reference.  
     BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates to an imaging optical system, and an imaging lens device incorporated with the imaging optical system.  
      2. Description of the Related Art  
      In recent years, with an explosive spread of digital apparatuses such as a digital still camera, a digital video camera, a mobile phone with a built-in camera (hereinafter, called as “camera phone”), and a personal digital assistant (PDA), development of a high-resolution or sophisticated image sensor to be loaded in these digital apparatuses has been rapidly progressed. In view of this, high optical performance is demanded for an imaging optical system for guiding an optical image of a subject to an image sensor in order to sufficiently utilize the performance of the high-resolution image sensor.  
      In addition to the above, portability is required in each of the digital apparatuses. There is proposed miniaturization of the imaging optical system as one measure for miniaturization of the digital apparatus. Conventionally, a collapsible mechanism has been adopted in the imaging optical system as one measure for miniaturization of the imaging optical system, for instance.  
      In the imaging optical system adopting the collapsible mechanism, the construction of a lens barrel is complicated, which may give rise to cost increase. Particularly, in a mechanism constructed such that a lens unit pops out in response to turning on of the power of the digital apparatus, it takes a certain time to finalize a shooting preparatory operation. Accordingly, a user may fail to release the shutter at a right moment to capture a scene.  
      There is known a technique of eliminating a reflecting surface on an optical path of an imaging optical system, as another measure for miniaturizing the imaging optical system. Various arrangements have been proposed in the imaging optical system. For instance, Japanese Unexamined Patent Publication No. 2002-196243 or counterpart U.S. Pat. No. 6,671,099B2 (called as “D1”) recites an imaging optical system provided with a first prism and a second prism each made of a medium having a refractive index of larger than 1.3, wherein the optical system comprises, in the order from the object side, a front unit including the first prism, an aperture stop, and a rear unit including the second prism, and the optical system is constructed not to form an intermediate image. Japanese Unexamined Patent Publication No. 2000-171716 (called as “D2”) proposes an imaging optical system having a reflecting surface, wherein an optical path is folded for the purpose of producing a compact and thin optical system. Japanese Unexamined Patent Publication No. HEI 9-211331 (called as “D3”) discloses an optical system provided with an optical device, wherein the optical system comprises, in the order of propagating an incident ray from an object, a first refracting surface serving as an incident surface, a convex mirror inclined relative to a reference axis of the first refracting surface, a concave mirror which serves as a second reflecting surface and is inclined relative to the reference axis, and a second refracting surface having a negative optical power.  
      Further, Japanese Unexamined Patent Publication No. 2004-70235 (called as “D4”) discloses an imaging optical system, wherein an optical axis is bent by 90 degrees by fixedly arranging a triangular prism in a lens group closest to an object or a subject, and a surface of the triangular prism for passing incident light is an aspherical concave surface. Japanese Unexamined Patent Publication No. 2004-170707 or counterpart U.S. patent application Publication No. 2004/0095503A1 (called as “D5”) discloses a technique of miniaturizing an imaging optical system by providing two reflecting surfaces for bending an optical axis by 90 degrees, wherein the bending direction is “twisted” in the space. Japanese PCT Publication (tokuhyo) 2000-515255 or counterpart U.S. Pat. No. 6,850,279B1 (called as “D6”) discloses a technique of miniaturizing an optical system by providing two reflecting elements, namely, mirrors for bending an optical axis by 90 degrees in a fixed focal length optical system. Japanese Unexamined Patent Publication No. 2004-247887 (called as “D7”) discloses a technique of miniaturizing an optical system by providing two reflecting elements such as a triangular prism or a mirror for bending an optical axis by 90 degrees.  
      In the documents D1 through D7, the following points should be considered. Specifically, in the imaging optical system recited in D1, all the prisms are decentered optical systems having an optical power on a reflecting surface thereof. Decentered aberrations are likely to occur in a decentered optical system unlike an axially symmetrical optical system. Accordingly, a conventional facility for use in production and evaluation of axially symmetrical optical systems cannot be used for a decentered optical system, and a new facility is required. Further, since a multitude of aberrations to be corrected occur in the decentered optical system, it is extremely difficult to produce an imaging optical system based on the decentered optical system. In addition to this, since the decentered optical system has two reflecting surfaces in each of which an error sensitivity due to its decentering is theoretically assumed to be about 4 times as high as a refractive optical system, high positional precision is required on these two reflecting surfaces.  
      In the imaging optical system recited in D2, the image sensor is arranged at a specified position in an attempt to produce a thin imaging optical system. Generally, it is difficult to produce a thin imaging optical system because a sufficient space is required for a wiring or the like to be provided in the vicinity of an image sensor.  
      Similarly to the imaging optical system recited in D1, the imaging optical system recited in D3 involves difficulty in production of a prism. Further, since merely a single reflecting prism having two reflecting surfaces is provided in the imaging optical system in D3, the optical system has difficulty in compatibility with an image sensor having several million pixels, although it has an optical performance compatible with an image sensor of several hundred thousand pixels.  
      In the imaging optical system recited in D4, since the optical axis is bent once, the thickness of the camera incorporated with the imaging optical system is determined by the size of the image sensor. Generally, parts such as a wiring, a circuit, and a packaging unit are arranged in the periphery of a light receiving surface of an image sensor, and the areas of these parts are considerably large as compared with the area of the light receiving surface. Therefore, the arrangement of D4 needs further improvement for miniaturization.  
      The zoom optical system recited in D5 has two reflecting surfaces for bending the optical axis by 90 degrees. However, the bending direction is “twisted” in the space. Accordingly, as in the case of D4, the thickness of the camera loaded with the optical system is determined by the size of the image sensor, and the arrangement of D5 needs further improvement for miniaturization.  
      In the optical system recited in D6, the thickness of the camera is determined by the thickness of the optical system. However, since the optical axis is bent by using a reflecting mirror, the required optical path is long as compared with the case of using a prism. As a result, the thickness of the optical system at a portion where the optical axis is bent is increased.  
      Further, although a prism is used for bending the optical axis in the optical system recited in D7, the prism is a triangular prism of a simple construction. Further, since a lens element is provided on the object side outside of the prism, the arrangement of D7 needs further improvement for miniaturization.  
      As mentioned above, the optical systems disclosed in D1 through D7 may lead to cost rise, and production of a compact imaging optical system having a high performance is difficult. In addition to these drawbacks, D4 through 7 are silent about a point that an arrangement relation between an exit surface of a reflecting prism and a light receiving surface of an image sensor is essentially important in miniaturizing an optical system provided with a reflecting prism, as shown in the arrangements of D4 through D7.  
     SUMMARY OF THE INVENTION  
      It is an object of the present invention to provide an imaging optical system and an imaging lens device which are free from the problems residing in the prior art.  
      It is another object of the present invention to provide an imaging optical system which is inexpensive and compact, and has a high optical performance, and is loadable in a thin mobile phone or a thin personal digital assistant by optimizing an arrangement relation between an exit surface of a reflecting prism and a light receiving surface of an image sensor, and an imaging lens device incorporated with such imaging optical system.  
      According to an aspect of the invention, an imaging optical system forms an optical image of a subject on a light receiving surface of an image sensor for converting the optical image into electrical signals. The imaging optical system is provided with two reflecting prisms each of which is adapted to bend incident light at a predetermined angle for reflection. An incident surface of the reflecting prism disposed on the side of the subject on an optical path, and an exit surface of the other reflecting prism are aligned substantially parallel to each other. The incident surface or the exit surface of the at least one of the reflecting prisms has an optical power.  
      In this imaging optical system, the two reflecting prisms each adapted for bending the incident light at the predetermined angle for reflection are arranged in such a manner that the incident surface of the reflecting prism disposed on the subject side on the optical path, and the exit surface of the other reflecting prism are aligned substantially parallel to each other. This arrangement enables to provide an inexpensive and compact imaging optical system.  
      Another aspect of the invention is directed to an imaging optical system comprising: a reflecting prism which reflects incident light at about 90 degrees; and an image sensor which has a light receiving surface opposing to an exit surface of the reflecting prism, and converts an optical image of a subject into electrical signals, wherein an arrangement relation between the exit surface of the reflecting prism and the light receiving surface of the image sensor satisfies the conditional formula (1): 
 
0.0 ≦d/a &lt;0.8   (1) 
 
 where a represents a height of the light receiving surface of the image sensor on a plane where an optical path of the imaging optical system is folded, and d represents a distance between the exit surface of the reflecting prism and the light receiving surface of the image sensor, the distance d including a physical distance in a case that an optical component is provided between the exit surface of the reflecting prism and the light receiving surface of the image sensor. 
 
      In this imaging optical system, the arrangement relation between the exit surface of the reflecting prism and the light receiving surface of the image sensor is optimized to miniaturize the imaging optical system incorporated with the image sensor. This arrangement enables to provide a thin digital apparatus incorporated with the imaging optical system.  
      These and other objects, features and advantages of the present invention will become more apparent upon reading of the following detailed description along with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIGS. 1A and 1B  are cross-sectional views schematically each showing  FIG. 1A  shows an imaging optical system incorporated with two reflecting prisms, and  FIG. 1B  shows an imaging optical system incorporated with a single reflecting prism which opposes a light receiving surface of an image sensor.  
       FIG. 2  is an illustration explaining an exit pupil distance.  
       FIGS. 3A and 3B  are optical path diagrams each showing a relation between an incident side prism and a light ray, wherein  FIG. 3A  shows a prism which does not have an optical power, and  FIG. 3B  shows a prism having an optical power.  
       FIGS. 4A and 4B  are cross-sectional views each showing an imaging side prism provided with an infrared cutting function, wherein  FIG. 4A  shows an example that an infrared reflecting film is integrally formed on an exit surface of an imaging side prism, and  FIG. 4B  shows an example that an infrared absorbing film is integrally formed on a reflecting surface of an imaging side prism.  
       FIG. 5  is a perspective view depicting the imaging optical system shown in  FIG. 1A  in a stereoscopic manner.  
       FIG. 6  is a schematic optical path diagram of the imaging optical system shown in  FIG. 5 .  
       FIG. 7  is a cross-sectional view schematically showing an arrangement of a zoom optical system as another embodiment of the imaging optical system embodying the invention.  
       FIGS. 8A through 8C  are external schematic views each showing a camera phone loaded with the inventive imaging optical system or the inventive zoom optical system, wherein  FIG. 8A  shows an external appearance of an operating face of the camera phone loaded with the imaging optical system,  FIG. 8B  shows an external appearance of a back face of the camera phone loaded with the imaging optical system is loaded, and  FIG. 8C  shows an external appearance of the camera phone loaded with the zoom optical system.  
       FIGS. 9A and 9B  are external schematic views each showing a foldable camera phone, wherein  FIG. 9A  shows an external appearance of an operating face of the camera phone, and  FIG. 9B  shows an external appearance of a back face of the camera phone.  
       FIGS. 10A and 10B  are external schematic views each showing a portable digital assistant, wherein  FIG. 10A  shows an external appearance of an operating face of the portable digital assistant, and  FIG. 10B  shows an external appearance of a back face of the portable digital assistant.  
       FIG. 11  is an illustration showing an arrangement of optical devices in a first embodiment of the inventive imaging optical system with an infinite focal length.  
       FIG. 12  is an illustration showing an arrangement of an imaging optical system, wherein a lens element having a function substantially equivalent to the function of a reflecting prism shown in  FIG. 11  is used in place of the reflecting prism.  
       FIG. 13  is an illustration showing an arrangement of an imaging optical system, wherein a prism is provided in place of the lens element disposed on the object side on the optical path in  FIG. 12 .  
       FIG. 14  is an illustration showing an arrangement of optical devices in a second embodiment of the inventive imaging optical system with an infinite focal length.  
       FIG. 15  is an illustration showing an arrangement of an imaging optical system, wherein a lens element having a function substantially equivalent to the function of a reflecting prism shown in  FIG. 14  is used in place of the reflecting prism.  
       FIG. 16  is an illustration showing an arrangement of optical devices in a third embodiment of the inventive imaging optical system with an infinite focal length.  
       FIG. 17  is an illustration showing an arrangement of an imaging optical system, wherein a lens element having a function substantially equivalent to the function of a reflecting prism shown in  FIG. 16  is used in place of the reflecting prism.  
       FIGS. 18A through 18F  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the imaging optical system in accordance with the first embodiment.  
       FIGS. 19A through 19F  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the imaging optical system in accordance with the second embodiment.  
       FIGS. 20A through 20F  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the imaging optical system in accordance with the third embodiment.  
       FIG. 21  is a cross-sectional view of a fourth embodiment of the imaging optical system, namely, a zoom optical system taken along a longitudinal direction of an optical axis in  FIG. 21 .  
       FIG. 22  is a cross-sectional view of a zoom optical system taken along a longitudinal direction of an optical axis shown in  FIG. 22 , wherein a lens element having a function substantially equivalent to the function of a reflecting prism in  
       FIG. 21  is used in place of the reflecting prism.  
       FIG. 23  is a cross-sectional view of a fifth embodiment of the imaging optical system, namely, a zoom optical system taken along a longitudinal direction of an optical axis in  FIG. 23 .  
       FIG. 24  is a cross-sectional view of a zoom optical system taken along a longitudinal direction of an optical axis shown in  FIG. 24 , wherein a lens element having a function substantially equivalent to the function of a reflecting prism in  
       FIG. 23  is used in place of the reflecting prism.  
       FIG. 25  is a cross-sectional view of a sixth embodiment of the imaging optical system, namely, a zoom optical system taken along a longitudinal direction of an optical axis in  FIG. 25 .  
       FIG. 26  is a cross-sectional view of a zoom optical system taken along a longitudinal direction of an optical axis shown in  FIG. 26 , wherein a lens element having a function substantially equivalent to the function of a reflecting prism in  FIG. 25  is used in place of the reflecting prism.  
       FIGS. 27A through 27I  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the zoom optical system in accordance with the fourth embodiment with an infinite focal length.  
       FIGS. 28A through 28I  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the zoom optical system in accordance with the fifth embodiment with an infinite focal length.  
       FIGS. 29A through 29I  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the zoom optical system in accordance with the sixth embodiment with an infinite focal length.  
       FIGS. 30A through 30I  are aberration diagrams regarding spherical aberrations, astigmatisms, and distortion aberrations of lens groups in the zoom optical system in accordance with the sixth embodiment with a closest focal length. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION  
     Description on Arrangement of Imaging Optical System  
       FIG. 1A  is an illustration schematically showing an arrangement of an imaging optical system  100  embodying the invention. The imaging optical system  100  is adapted to form an optical image of a subject H on a light receiving surface of an image sensor  105  which converts the optical image into electrical signals. The imaging optical system  100  has two reflecting prisms each adapted to bend an incident ray at a certain degree, e.g., about 90 degrees, for guiding the reflected ray in a predetermined direction. Specifically, the imaging optical system  100  has a first reflecting prism  101  disposed on the side of the subject H on the optical path (hereinafter, also called as “incident side prism  101 ”), and a second reflecting prism  102  disposed on the side of the image sensor  105  on the optical path (hereinafter, also called as “imaging side prism  102 ”). A lens element  103  for focusing, and an aperture stop  104  are arranged between the incident side prism  101  and the imaging side prism  102  according to needs.  
      An incident surface  101   a  of the incident side prism  101  and an exit surface  102   b  of the imaging side prism  102  are disposed substantially parallel to each other. Specifically, an optical axis AX from the subject H to the image sensor  105  is bent on a reflecting surface  101   c  of the incident side prism  101  at about 90 degrees, and then bent on a reflecting surface  102   c  of the imaging side prism  102  at about 90 degrees. The imaging optical system  100  is housed in an apparatus housing BD of a variety of digital apparatuses such as a mobile phone.  
      In the imaging optical system  100  having the above construction, at least one of the incident surface  101   a  of the incident side prism  101  and an incident surface  102   a  of the imaging side prism  102 , or at least one of an exit surface  101   b  of the incident side prism  101  and the exit surface  102   b  of the imaging side prism  102  has an optical power. For instance, the incident surface  101   a  or the exit surface  101   b  of the incident side prism  101 , and/or the incident surface  102   a  or the exit surface  102   b  of the imaging side prism  102  has an optical power. Alternatively, the incident surface  101   a  of the incident side prism  101  and the incident surface  102   a  of the imaging side prism  102 , or the exit surface  101   b  of the imaging side prism  101  and the exit surface  102   b  of the imaging side prism  102  may have an optical power. In any of the arrangements, at least one of the incident surfaces  101   a,    102   a,  or at least one of the exit surfaces  101   b,    102   b  is utilized as a surface having a function of a lens element. Accordingly, this arrangement enables to obviate use of an additional optical device, which contributes to production of a compact imaging optical system.  
      The image sensor  105  photoelectrically converts an optical image of the subject H formed by the imaging optical system  100  into image signals of red (R), green (G), and blue (B) components in accordance with the light amount of the optical image for outputting the image signals to a specified image processing circuit. An example of the image sensor  105  is a single CCD color area sensor of a so-called “Bayer matrix” in which patches of color filters each in red (R), green (G), and blue (B) are attached on respective surfaces of charge coupled devices (CCDs) arrayed in two dimensions. A CMOS image sensor, a VMIS® image sensor produced by Innotech Corporation, and a like sensor are usable as the image sensor in addition to the CCD color area sensor.  
      In the case where the image sensor  105  is of a rectangular shape having a longer side and a shorter side, it is preferable that a light ray is bent in the shorter side direction of the image sensor  105 , namely, in the direction of the arrows a in  FIG. 1A . It is possible to reduce the thickness of the imaging optical system  100  to some extent by bending a light ray in the longer side direction of the image sensor  105 . However, designing the optical system in such a manner as to bend a light ray in the shorter side direction of the image sensor  105  is advantageous in producing a thin imaging optical system.  
      In the imaging optical system  100  having the above construction, an arrangement relation between the exit surface  102   b  of the imaging side prism  102  and the light receiving surface of the image sensor  105  is optimized. Specifically, in  FIG. 1A , the size of the imaging optical system  100  in the direction of the arrows A can be reduced by matching the moving direction of the focusing lens element  103  and the arranged direction of an image sensor holder (not shown) including the image sensor  105  which requires a certain width, with the widthwise direction of the apparatus housing BD. However, in the arrangement that the image sensor  105  is housed in the apparatus housing BD with the exit surface  102   b  of the imaging side prism  102  opposing to the image sensor  105 , it is desirable to minimize the distance between the exit surface  102   b  of the imaging side prism  102  and the image sensor  105  to reduce the thickness of the apparatus housing BD.  
      Now, let us assume that d represents a distance between the exit surface  102   b  of the imaging side prism  102  and the light receiving surface of the image sensor  105 , the distance d including a physical distance in a case that an optical component is arranged between the imaging side prism  102  and the image sensor  105 , and a represents a height of the light receiving surface of the image sensor  105  on a plane where the optical path of the imaging optical system  100  is folded, which corresponds to the plane of  FIG. 1A , e.g., the size of the image sensor  105  in the shorter side direction thereof. Then, in the embodiment of the invention, an arrangement relation between the exit surface  102   b  of the imaging side prism  102  and the image sensor  105  as defined by the conditional formula (1) is established. This arrangement enables to miniaturize the apparatus housing BD in the thickness direction thereof 
 
0.0≦ d/a&lt; 0.8   (1) 
 
      In the above formula (1), if d/a is 0.8 or larger the distance d between the exit surface  102   b  of the imaging side prism  102  and the light receiving surface of the image sensor  105  becomes too large, which obstructs reducing the thickness of the apparatus housing BD. In other words, a large distance d means a large imaging side prism for forming an optical image on the light receiving surface of the image sensor  105 . As a result, the thickness of the imaging optical system  100  is increased as a whole.  
      On the other hand, the arrangement of d/a=0, namely, the arrangement of contacting the exit surface  102   b  of the imaging side prism  102  with the light receiving surface of the image sensor  105  may be a preferred arrangement in minimizing the size of the imaging optical system  100  in the direction of the arrows A. However, contact of the exit surface  102   b  with the light receiving surface of the image sensor  105  may give rise to difficulty in assembling. In addition to this drawback, there is likelihood that a ghost image may appear by plane reflection between the exit surface  102   b  and the light receiving surface of the image sensor  105 . In order to avoid these drawbacks, it is desirable to set the lower limit of d/a at 0.1 or larger.  
      The imaging optical system  100  shown in  FIG. 1A  is an example of an optical system in which two reflecting prisms are used to bend an incident ray at about 90 degrees twice, so that the incident surface  101   a  of the incident side prism  101  is aligned substantially parallel to the exit surface  102   b  of the imaging side prism  102 . In the embodiment of optimizing the arrangement relation between the exit surface  102   b  of the imaging side prism  102  and the light receiving surface of the image sensor  105 , it is possible to use three or more reflecting prisms to form an optical path for guiding light in two dimensional or three dimensional manner in the apparatus housing BD. In such an arrangement, the incident surface  101   a  and the exit surface  102   b  may be or may not be aligned substantially parallel to each other.  
      Further alternatively, as shown in an imaging optical system  100 ′ shown in  FIG. 1B , it is possible to arrange merely an imaging side prism  102  on the side of a light receiving surface of an image sensor  105 . In the imaging optical system  100 ′, the optical axis AX from the subject H to the image sensor  105  is bent at about 90 degrees on a reflecting surface  102   c  of the imaging side prism  102  through an incident lens element  107 . In this way, various optical arrangements are applicable to the embodiment of the invention. In the following section, the embodiment is described primarily based on the imaging optical system  100  shown in  FIG. 1A .  
      Next, a preferred optical arrangement of the imaging optical system  100  is described from various aspects. As mentioned above, the thickness of the imaging optical system  100  can be reduced not only by setting the arrangement relation between the exit surface  102   b  of the imaging side prism  102  and the image sensor  105  as defined above, but also by optimizing the size or the length of the imaging side prism  102 . As shown in  FIG. 2 , it is desirable to satisfy the conditional formula (2) where n represents a refractive index of the imaging side prism  102 , t represents a distance of a principal ray on the optical axis AX propagating through the imaging side prism  102 , namely, a thickness of the imaging side prism  102  in an expanded state thereof, and p represents an exit pupil distance. 
 
−1.5&lt;( t·n )/ p&lt; 1.0   (2) 
 
      In the formula (2), if (t·n)/p is 1.0 or more, since the exit pupil distance p becomes long relative to the size of the imaging side prism  102 , the optical system is closer to a telecentric optical system. As a result, the width of light rays propagating in the imaging side prism  102  is increased, and the size or the length of the imaging side prism is unduly increased in order to allow the light rays of such a large width to repetitively propagate through the imaging side prism. Consequently, such an arrangement leads to failure of miniaturization of the imaging optical system  100 .  
      On the other hand, if (t·n)/p is −1.5 or less, the exit pupil distance p becomes short relative to the size of the imaging side prism  102 . As a result, the optical system is likely to pass a light ray of a large inclination with respect to the optical axis, contrary to a telecentric optical system. Generally, a micro lens element is arranged per pixel on the light receiving surface of the image sensor  105  to raise light focusing efficiency. In the case of a telecentric optical system, a micro lens element can be arranged substantially right above each pixel, which is a relatively easy operation. However, if the exit pupil distance p is short, and a light ray propagates with a large inclination with respect to the optical axis, it is necessary to arrange a micro lens element at a displaced position relative to each pixel, considering the inclination. If a light ray propagates with a large inclination due to a value of (t·n)/p smaller than the lower limit of the formula (2), it is difficult to arrange micro lens elements at intended positions to secure a required light amount for focusing. In such an arrangement, light focusing efficiency may be lowered, and the light amount around the micro lens elements may be reduced.  
      Further, a short exit pupil distance p means a short distance between the aperture stop  104  and the light receiving surface of the image sensor  105 . In view of a fact that it is impossible to arrange the aperture stop  104  on the imaging side relative to an incident surface  102   a  of the imaging side prism  102 , namely, it is impossible to provide an aperture stop inside a prism, it is difficult to dispose the aperture stop  104  at an appropriate position if the value of (t·n)/p is smaller than the lower limit of the formula (2).  
      The following advantages are obtained in the arrangement as shown in  FIG. 1A , in which the aperture stop  104  is disposed on the side of the exit surface  101   b  of the incident side prism  101 , and the incident surface  101   a  of the incident side prism  101  has a negative optical power.  FIGS. 3A and 3B  are optical path diagrams each showing a relation between an incident side prism and a light ray. In the case where light rays having a certain width BT are allowed to go out of the incident side prism, it is preferable that an exit ray op-out propagating in an outermost peripheral region of the prism goes out from the prism substantially in parallel with the optical axis AX to miniaturize the prism itself.  
      Specifically, as shown in  FIG. 3A , in the case where an incident surface  101   a ′ of an incident side prism  101 ′ is flat, it is impossible to minimize an incident angle θ 1  of an incident ray op-in which is incident onto the incident surface  101   a ′ and propagates in an outermost peripheral region of the prism  101 ′ relative to the optical axis AX. As a result, the exit ray op-out goes out of the prism  101 ′ with a certain inclination relative to the optical axis AX. In such an arrangement, it is required to increase the areas of the incident surface  101   a ′ and an exit surface  101   b ′, considering the inclination, to secure a certain light width BT, which may cause size increase of the prism.  
      On the other hand, as shown in  FIG. 3B , in the case where an incident surface  101   a  of an incident side prism  101  is concaved and has a negative optical power, an incident angle θ 2  of an incident ray op-in which is incident onto the incident surface  101   a  and propagates in an outermost peripheral region of the incident side prism  101  is small relative to the optical axis AX. As a result, an exit ray op-out goes out of the prism  101  substantially parallel to the optical axis AX. This arrangement enables to remarkably reduce the size of the prism for securing a certain light width BT and contributes to miniaturization of the imaging optical system  100 , as compared with the arrangement as shown in  FIG. 3A .  
      Further, as shown in the imaging optical system  100  in  FIG. 1A , it is preferable to arrange an optical device having a refractive power or an optical power on the optical path between the incident surface  101   a  of the incident side prism  101  and the exit surface  102   b  of the imaging side prism  102  without arranging an optical device having a refractive power or an optical power on the optical path on the side of the subject H relative to the incident surface  101   a  of the incident side prism  101  or on the optical path on the side of the image sensor  105  relative to the exit surface  102   b  of the imaging side prism  102 . As compared with the arrangement that an optical device having a refractive power is arranged on the optical path on the side of the subject H relative to the incident surface  101   a  of the incident side prism  101 , this arrangement enables to reduce the thickness of the imaging optical system  100  in the direction of the arrows A, which contributes to miniaturization of the imaging optical system  100 .  
      Further, in the imaging optical system  100 , it is preferable to arrange a lens element or a lens group between the incident side prism  101  and the imaging side prism  102  to correct field curvature, aberration or a like drawback and to improve optical performance of the imaging optical system  100 . In arranging the lens element or the like, a drawback of unduly increasing the size of the optical system in the direction of the arrows A resulting from loading of the lens element can be avoided by adopting a lens element having a size smaller than the reflecting prism in the direction of the arrows A.  
      It is preferable to drive the lens element or the lens group in an optical axis direction thereof, namely, in a direction substantially parallel with the incident surface  101   a  of the incident side prism  101  for focusing for the following reason. If the entirety of an imaging optical system including a reflecting prism is driven in the optical axis direction, such an arrangement may give rise to drawbacks such as size increase of a drive motor due to increase of the weight of a device to be driven, non-alignment of the optical axis by the driving, and complexity of a mechanism for supporting the optical devices of the imaging optical system. Arranging a lens element or a lens group between the two reflecting prisms enables to securely hold the reflecting prisms and the aperture stop, and driving the lens element or the lens group in the optical axis direction enables to eliminate various drawbacks such as size increase of a drive motor, occurrence of non-alignment of the optical axis, and complexity of an optical device supporting mechanism.  
      In the imaging optical system  100  as shown in  FIG. 1A , the focusing lens element  103  is arranged between the incident side prism  101  and the imaging side prism  102  to satisfy the above requirements. In other words, focusing is implemented by driving the focusing lens element  103  in a direction parallel to the incident surface  101   a  of the incident side prism  101 .  
      In the imaging optical system  100 , it is preferable to make the optical surfaces of the respective optical devices of the imaging optical system  100  symmetrical to each other with respect to the optical axis AX, namely, rotationally symmetrical to each other in light of feasibility of production of the optical devices such as the incident side prism  101 , the imaging side prism  102 , and the lens element  103 . An axially asymmetrical optical system is not desirable because production of such an optical system is difficult, and production cost may rise, considering evaluation in assembling and difficulty in adjustment. However, it is possible to use axially asymmetrical surfaces as reflecting surfaces, as far as cost increase is permissible.  
      There is a case that if a CCD image sensor or a CMOS image sensor is used as the image sensor  105 , an infrared component may cause a noise, which may degrade an output image. In view of this, a measure of arranging an infrared cut filter or a like element at an appropriate position of an imaging optical system has been conducted to keep an infrared component from being incident onto the image sensor  105 . However, such a measure requires an optical component having an infrared blocking function as an additional part, which may hinder miniaturization of the imaging optical system, and reduction of the number of parts.  
      In view of the above, it is desirable to provide the imaging side prism  102  itself with an infrared blocking function of reducing or removing an infrared component included in an incident ray.  FIGS. 4A and 4B  are cross-sectional views each showing an example of an imaging side prism  102  equipped with an infrared blocking function.  FIG. 4A  shows an example that an infrared reflecting film  102   d  is integrally formed on an exit surface  102   b  of an imaging side prism  102 . In this arrangement, an infrared component included in an incident ray is reflected by the infrared reflecting film  102   d  to thereby keep the infrared component from being incident onto an image sensor  105 . A preferred example of the infrared reflecting film  102   d  is an inductive multilayer coating which reflects light in the range of an infrared wavelength. It is possible to attach the infrared reflecting film  102   d  on the incident surface  102   a  of the imaging side prism  102 .  
       FIG. 4B  shows an example that an infrared absorbing film  102   e  is integrally formed on a reflecting surface  102   c  of an imaging side prism  102 . In this arrangement, an infrared component included in an incident ray is absorbed by the infrared absorbing film  102   e  to thereby keep the infrared component from being incident onto an image sensor  105 . A preferred example of the infrared absorbing film  102   e  is an inductive multilayer coating which absorbs light in the range of an infrared wavelength. It is possible to attach an infrared transparent film on the reflecting surface  102   c  to pass merely an infrared component through the imaging side prism  102 .  
      Next, materials and production methods of the incident side prism  101  and the imaging side prism  102  are described. There is no specific limit to the material for the prisms  101  and  102 . An optical material having a certain light transparency or a certain refractive index such as various kinds of glass materials, and resins (plastic) materials is usable. Use of a resin material is advantageous, as compared with a case of using a glass material, in the aspect of production cost and production of a lightweight imaging optical system, because use of the resin material enables to realize mass-production of lightweight prisms by injection molding or a like technique. Further, in the case of producing a reflecting prism with an incident surface and/or an exit surface having a refractive power, as mentioned above, a grinding process is necessary, if the reflecting prism is made of a glass material. Compared with use of a glass material, use of a resin material is advantageous because a reflecting prism can be easily produced with use of a mold form or a like device.  
      Production of optical components having high precision may be difficult according to injection molding, because heat shrinkage of some extent is unavoidable after the molding. The imaging side prism  102  requires less precision as compared with the incident side prism  101 , because the imaging side prism  102  is disposed closer to the image sensor  105 , and error sensitivity thereof is relatively small. In view of this, it is desirable to make at least the imaging side prism  102  of a resin material, and to make the incident side prism  101  of a resin material or a glass material depending on a required precision.  
      In the case of making the incident side prism  101  and/or the imaging side prism  102  of a resin material, it is possible to use various optical resin materials such as polycarbonate and polymethyl methacrylate (PMMA) as the resin material. Among these, it is desirable to use a resin material having a water absorption coefficient of 0.01% or smaller. A resin material has a moisture absorption power of bonding with water components in the air. If such a moisture absorption power is acted, optical characteristics such as a refractive index may be changed even if the prism is fabricated as designed. In view of this, the imaging optical system  100  free of moisture absorption power can be produced by using a resin material having a water absorption coefficient of 0.01% or less. An example of the resin material having a water absorption coefficient of 0.01% or less is available under the trade name of ZEONEX® produced by Zeon Corporation.  
      Examples of the method for producing a prism with an incident surface and/or an exit surface having an optical power include cementing a lens element having an optical power with a predetermined prism, grinding a prism to make a curved surface, an injection molding technique, and a glass molding technique. In the technique of cementing a lens element with a prism or in the technique of grinding a prism into a curved surface, axial alignment is required to adjust a positional relation of the reflecting surface of the prism to the lens element to be cemented or to the curved surface of the prism, or an inclination of the prism and the lens element relative to the optical axis, which may make the production process complicated. As compared with the above, an injection molding technique with use of a resin material is preferred because of its superior mass-productivity.  
      It is desirable to consider the following points in adopting a prism produced by the injection molding. In conducting the injection molding, a gate is necessary for injecting a resin material into a mold. The gate may oppose to any surface of a prism to be molded. However, preferably, the gate may be arranged at a surface of the prism other than a surface used for light incidence, emergence, and reflection. This arrangement is preferred because generally, birefringence is likely to occur on or around the site of the prism where the gate is arranged because trace of resin flow is likely to be formed on the gate arranged site of the prism, which may give adverse effects to optical characteristics of the resultant prism. Arranging the gate at a surface of the prism other than the surface used for light incidence, emergence, and reflection enables to reduce an influence of birefringence, even if birefringence occurs.  
       FIG. 5  is a perspective view of the imaging optical system  100  shown in  FIG. 1A  depicted in a stereoscopic manner. A preferred arrangement of the imaging optical system  100  provided with a prism produced by the injection molding is described referring to  FIG. 5 . Referring to  FIG. 5 , in forming the incident side prism  101  by the injection molding, a gate for injecting a resin material into a mold is arranged at an unused surface  101   m,  which is a surface of the prism other than the incident surface  101   a,  the exit surface  101   b,  and the reflecting surface  101   c.  Generally, since a gate has a prismatic configuration of a rectangular shape in cross section, a gate trace Ge 1  of a prismatic configuration having a surface of a broad width parallel with the incident surface  101   a  is formed on the unused surface  101   m.  It should be noted that the gate trace Ge 1  is illustrated with a larger magnification than the other parts. Arranging the gate in the above-mentioned manner enables to reduce an influence of birefringence which may affect an effective usable area pw 1  of the incident side prism  101  shown by the hatched portions in  FIG. 5  where light rays are allowed to propagate, even if birefringence occurs in the vicinity of the gate trace Ge 1 .  
      Similarly to the incident side prism  101 , the imaging side prism  102  is produced by arranging a gate for injecting a resin material into a mold at an unused surface  102   m,  which is a surface of the prism other than the incident surface  102   a,  the exit surface  102   b,  and the reflecting surface  102   c.  In this case, a gate trace Ge 2  of a prismatic configuration having a surface of a broad width parallel with the reflecting surface  102   c  is formed on the unused surface  102   m.  Arranging the gate in the above-mentioned manner enables to reduce an influence of birefringence which may affect an effective usable area pw 2  of the imaging side prism  102  shown by the hatched portion in  FIG. 5 , even if birefringence occurs in the vicinity of the gate trace Ge 2 .  
      It is a common practice to pressingly take out a molded product, in this case, a prism from the mold with use of eject pins after the injection molding. In this case, traces of the eject pins are also likely to be formed in a site of the prism where the eject pins have been contacted, and optical characteristics may be varied on or around the trace forming site. In the example shown in  FIG. 5 , eject pins are arranged at a site corresponding to an unused area of the incident surface  101   a  of the incident side prism  101 , so that traces ep 1  of the eject pins appear on the unused area. Likewise, eject pins are arranged at a site corresponding to an unused area of the reflecting surface  102   c  of the imaging side prism  102 , so that traces ep 2  of the eject pins appear on the unused area. Alternatively, it is possible to arrange eject pins in such a manner that traces ep 1  of the eject pins for the incident side prism  101  appear on an unused surface  101   n  opposite to the unused surface  101   m,  and traces ep 2  of the eject pins for the imaging side prism  102  appear on an unused surface  102   n  opposite to the unused surface  102   m.    
      In the case where the aperture stop  104  is arranged between the incident side prism  101  and the imaging side prism  102  as shown in the imaging optical system  100  of  FIG. 1A , it is desirable to arrange the gates at such a position that the gate trace Ge 1  on the incident side prism  101  and the gate trace Ge 2  on the imaging side prism  102  extend in the same direction, as shown in  FIG. 5 , in assembling the prisms  101 ,  102  in the apparatus housing BD. This is described referring to  FIG. 6 .  
       FIG. 6  is a schematic optical path diagram of the imaging optical system  100  shown in  FIG. 5 . As illustrated in  FIG. 6 , the gate trace Ge 1  on the incident side prism  101  and the gate trace Ge 2  on the imaging side prism  102  are respectively formed on the unused surfaces  101   m  and  102   m  aligned in the same direction. The unused surfaces  101   n,    102   n  opposite to the unused surfaces  101   m,    102   m  are flat without formation of the gate traces Ge 1 , Ge 2 , namely, stable surfaces in configuration. Therefore, the unused surfaces  101   n,    102   n  are fixedly supported on a prism supporting member  106  commonly provided for the incident side prism  101  and the imaging side prism  102 . The prism supporting member  106  corresponds to a frame member of the apparatus housing BD or a like element. With this arrangement, the prisms  101 ,  102  can be assembled in the apparatus housing BD with high precision.  
      An influence of birefringence or a like phenomenon can be reduced to some extent, but cannot be completely removed by forming the gate traces Ge 1 , Ge 2  on the unused surfaces  101   m,    102   m,  respectively. Ge 1   m,  Ge 2   m  shown by the hatched portions in  FIG. 6  are gate affecting areas, which may affect optical characteristics of the incident side prism  101  and the imaging side prism  102  in the vicinity of the gate traces Ge 1 , Ge 2 , respectively.  
      In the case where the aperture stop  104  is arranged between the incident side prism  101  and the imaging side prism  102 , optical images turn upside down before and after passing the aperture stop  104 . Considering the optical path of an incident ray op which is incident onto the incident surface  101   a  of the incident side prism  101  from the side where the gate trace Ge 1  is formed, since the incident ray op passes through the gate affecting area Ge 1   m  in the incident side prism  101 , the incident ray op may be affected by birefringence or the like. The incident ray op, after passing the aperture stop  104 , is bent in a direction away from the gate trace Ge 1 . When the incident ray op is incident onto the imaging side prism  102 , the incident ray op propagates in the imaging side prism  102  in a region away from the gate affecting area Ge 2   m.  This arrangement keeps the incident ray op from passing both through the gate affecting area Ge 1   m  of the incident side prism  101  and the gate affecting area Ge 2   m  of the imaging side prism  102 . With this arrangement, an influence of residue birefringence can be alleviated, which eliminates likelihood that substantially a half region of a displayed image may be affected by an influence of birefringence or the like.  
      The injection molding using the resin material is suitable for mass production and is advantageous in forming a concave incident or exit surface of high precision in a reflecting prism. However, according to the injection molding, it is impossible to fabricate a reflecting prism having a high refractive index in light of a fact that a resin material is used. In view of this, it is desirable to fabricate a prism having a high refractive index and high precision according to glass molding by heating a glass material having a high refractive index in a mold having a shape of a prism under pressurization. Use of a prism having a high refractive index enables to shorten the optical path length and suppress generation of aberration on a refracting surface, which makes it possible to realize miniaturization of the imaging optical system  100 , and reduction of the number of lens elements, and is advantageous in producing a compact digital apparatus.  
       FIG. 7  is an illustration schematically showing another embodiment of the invention, specifically, a zoom optical system  110  capable of performing zooming operation, as an example of the imaging optical system. Similarly to the imaging optical system  100  as shown in  FIG. 1A , the zoom optical system  110  is designed to form an optical image of a subject H on a light receiving surface of an image sensor  105  which converts the optical image into electrical signals. The zoom optical system  110  has two reflecting prisms, namely, an incident side prism  101  disposed on the side of the subject H on the optical path, and an imaging side prism  102  disposed on the side of the image sensor  105  on the optical path. The zoom optical system  110  is different from the imaging optical system  100  in that a lens group  113  for zooming and focusing is provided between the incident side prism  101  and the imaging side prism  102  in addition to an aperture stop  104 .  
      The lens group  113  includes variable lens elements  1131  and  1132  which are movable in the directions of the arrows B 1  and B 2  in  FIG. 7 , respectively. Specifically, the variable lens elements  1131  and  1132  are driven for zooming in the optical axis direction of the lens group  113 , namely, in a direction substantially parallel to an incident surface  101   a  of the incident side prism  101 . This is to avoid the following drawbacks. If the entirety of a zoom optical system including a reflecting prism is driven in the optical axis direction, such an arrangement may give rise to drawbacks such as unduly increase of the thickness of the optical system due to change of the thickness of the entirety of the optical system, or size increase of a drive motor due to increase of the weight of a device to be driven. In addition to the above, there are drawbacks such as non-alignment of the optical axis due to the driving, and complexity of a mechanism for supporting the optical devices of the zoom optical system. Arranging a lens group between the two reflecting prisms and driving the lens group in the optical axis direction enables to fixedly support the reflecting prisms and the aperture stop, and to eliminate various drawbacks such as size increase of a drive motor, occurrence of non-alignment of the optical axis, and complexity of an optical device supporting mechanism.  
      Generally, in zooming, two lens groups, namely, a variator lens group and a compensator lens group are required to be moved. In view of this, preferably, at least two lens groups are arranged between the two prisms, with each of the lens groups being movable in the optical axis direction for an intended zooming operation. Moving the two lens groups individually along the optical axis direction enables to produce a thin and compact zoom optical system loadable into a mobile phone or a PDA, because this arrangement is free from a change of the thickness of the optical system in zooming. Further, moving both of the two lens groups enables to shorten the moving distance of the respective lens groups, as compared with an arrangement of moving a single lens group, which leads to miniaturization of the optical system. Alternatively, it is possible to move a single lens group in zooming by properly regulating a zoom resolution as in the case of an optical zoom system.  
      In the zoom optical system  100  as shown in  FIG. 7 , the variable lens elements  1131  and  1132  are arranged between the incident side prism  101  and the imaging side prism  102  to meet the above requirements. In other words, zooming is performed by moving the variable lens elements  1131  and  1132  in directions parallel to the incident surface  101   a  of the incident side prism  101 , namely, in the directions of the arrows B 1  and B 2 , respectively.  
      As in the case of the imaging optical system  100  as shown in  FIG. 1A , in the zoom optical system  110 , at least one of the incident surface  101   a  of the incident side prism  101  and the incident surface  102   a  of the imaging side prism  102 , or at least one of the exit surface  101   b  of the incident side prism  101  and the exit surface  102   b  of the imaging side prism  102  has an optical power. Further, there is established an arrangement relation between the exit surface  102   b  of the imaging side prism  102  and the light receiving surface of the image sensor  105 , as defined by the conditional formulae (1) and (2). In addition to this, the same idea as applied to the imaging optical system  100  is applied to the zoom optical system  110  regarding formation of a gate trace on a reflecting prism, and a preferred optical arrangement such as an arrangement as to how an optical power is given to a reflecting prism.  
     Description on Digital Apparatus Incorporated with Imaging Optical System  
      Next, a digital apparatus incorporated with the imaging optical system  100  or the zoom optical system  110  is described.  FIGS. 8A and 8B  are external schematic views of a camera phone  200  loaded with the imaging optical system  100 , and  FIG. 8C  is an external schematic view of a camera phone  220  loaded with the zoom optical system  110 . The camera phones  200  and  220  are examples of the inventive digital apparatus. In the embodiment of the invention, examples of the digital apparatus include a digital still camera, a digital video camera, a digital video unit, a personal digital assistant (PDA), a personal computer, a mobile computer, and peripheral devices thereof such as a mouse, a scanner, and a printer. The digital still camera or the digital video camera corresponds to an imaging lens device which converts, after optically reading a video image of a subject, the video image into electrical signals using a semiconductor device, and stores the electrical signals into a storage medium such as a flash memory. Further, in the embodiment of the invention, the digital apparatus includes a mobile phone, a PDA, a personal computer, a mobile computer, and peripheral devices thereof each having specifications of incorporating a compact imaging lens device for optically reading a still image or a video image of a subject.  
       FIG. 8A  shows an operating face of the camera phone  200 , and  FIG. 8B  shows a back face of the camera phone  200 . The camera phone  200  includes at an upper part thereof an antenna  201 , and on the operating face thereof a rectangular display  202  having a longer side Lt 1  extending in a vertical direction on the plane of  FIG. 8A , a mode switchover button  203  for activating the image shooting mode and for switching over the image shooting mode between still image shooting and moving image shooting, a shutter button  204 , and a dial button  205 .  
      In the case where a zoom optical system is incorporated in the camera phone  220  as shown in  FIG. 8C , a zoom button  210  for controlling zooming is provided on the operating face of the camera phone  220 . The symbol “T” indicating the telephoto limit of the optical system is marked on an upper end portion of the zoom button  210 , and the symbol “W” indicating the wide angle limit of the optical system is marked on a lower end portion of the zoom button  210 . The zoom button  210  is constituted of a two-contact switch constructed such that telephoto shooting or wide-angle shooting is allowed in response to pressing of the upper end portion or the lower end portion of the zoom button  210 .  
      An imaging lens device (camera)  206  including an imaging optical system  100 , and an image sensor  105  such as a CCD sensor are incorporated in the camera phone  200 . A taking lens element  207  of the imaging lens device  206  is exposed out of the back face of the camera phone  200  for receiving light representing an optical image of a subject. An incident surface  101   a  of an incident side prism  101  is arranged on the back face of the taking lens element  207 . In other words, the incident surface of the taking lens device  206  for passing incident light of a subject and the display  202  are arranged on the back face and the operating face of the camera phone  200 , respectively. With this arrangement, an image acquired through the taking lens device  206  can be captured while the image is displayed on the display  202 .  
      The image sensor  105  is of a rectangular shape with an aspect ratio of an imaging area at 4:3, for instance. An image sensor of a multi-purpose use is generally of a rectangular shape. It is desirable to incorporate the imaging lens device  206  including the image sensor  105  in the camera phone  200  as shown in  FIGS. 8A and 8B , considering the arrangement relation with the rectangular display  202 .  
      Specifically, in the case where the display  202  has the longer side Lt 1  extending in the vertical direction on the plane of  FIG. 8A , preferably, the image sensor  105  has a longer side Lt 2  extending in a vertical direction on the plane of  FIG. 8B . In other words, it is desirable to assemble the display  202  and the image sensor  105  in such a manner that the longer side Lt 1  of the display  202  and the longer side Lt 2  of the image sensor  105  are aligned parallel to each other in the same direction. Thereby, an optical image of a subject that has been incident through the taking lens device  207  and captured on the rectangular imaging area of the image sensor  105  is effectively displayed on the rectangular display  202 .  
      More specifically, if the longer side Lt 1  of the display  202  and the longer side Lt 2  of the image sensor  105  are aligned parallel to each other, the longer side direction of the image captured by the image sensor  105  and the longer side direction of the display image are coincident with each other. With this arrangement, an image can be effectively displayed on the display area of the display  202  to thereby enable to display the image enlargedly. In other words, this arrangement enables image display of maximally utilizing the display area of the display  202 , which is advantageous in confirming the image composition in image shooting or the like. The same idea is applied to the case that the zoom optical system is incorporated in the camera phone  220  as shown in  FIG. 8C .  
      The taking lens device  206  may include a plane parallel plate corresponding to an optical low-pass filter or the like, in addition to the imaging optical system  100  for forming an optical image of a subject. Examples of the optical low-pass filter include, for instance, a birefringent low-pass filter made of a crystal or a like material whose crystallographic axis direction has been regulated, and a phase-type low-pass filter capable of realizing required optical cutoff frequency characteristics by diffraction effect.  
      An optical low-pass filter may not be an essential element. Further alternatively, an infrared cut filter may be provided in place of an optical low-pass filter to reduce a noise included in an image signal outputted from the image sensor  105 . In this case, it is desirable that the reflecting prism has an infrared blocking function as mentioned above. Further alternatively, it is possible to allow a single element to exhibit functions of an infrared cut filter and an optical low-pass filter by applying infrared reflecting coat on a surface of an optical low-pass filter.  
      An image shooting operation of the camera phone  200  having the above construction is described below. In shooting a still image, the image shooting mode is activated by pressing the mode switchover button  203  one time. In this embodiment, depressing the mode switching button  203  one more time switches over the image shooting mode from the still image shooting mode to the moving image shooting mode. When the still image shooting mode is activated, a subject image is cyclically captured by the image sensor  105  such as a CCD sensor through the imaging lens device  206 . Then, after the acquired image data is transferred to a memory for display, the image is displayed on the display  202 . The photographer can move the subject image to an intended position within the display screen while viewing the image through the display  202 . When the photographer depresses the shutter button  204  with the subject image being located at the intended position, a still image of the subject is obtained. Thus, image data representing the captured still image is stored in a memory for storing the still image data.  
      In the case of conducting moving image shooting, after the still image shooting mode is activated by depressing the mode switching button  203  one time, the mode switching button  203  is depressed once again to change the image shooting mode to the moving image shooting. Thereafter, similarly to the still image shooting, the photographer views the subject image through the display  202  to move the subject image captured through the imaging lens device  206  to an intended position within the display screen. When the photographer depresses the shutter button  204  in this state, the photographer can start moving image shooting. When the photographer depresses the shutter button  204  again in this state, the moving image shooting is terminated. The captured moving image data is sent to a memory for displaying the moving image on the display  202 , and is also sent to a memory for storing the moving image data for storage.  
      On the other hand, in the case of the camera phone  220  incorporated with the zoom optical system as shown in  FIG. 8C , zoom shooting is operable. Specifically, when zoom shooting performed under the condition that a subject is located away from the photographer, or the photographer wishes to capture the subject enlargedly, the photographer depresses the upper end portion of the zoom button  210  where the symbol “T” is marked. Then, the state that the zoom button  210  is being depressed toward the telephoto limit is detected, and a lens driving for zooming is executed for a time duration while the zoom button  210  is depressed to carry out continuous zooming. If the photographer wishes to reduce the magnification of the subject image to life-size magnification, for example, in an excessive zooming, the photographer depresses the lower end portion of the zoom button  210  where the symbol “W” is marked. Then, the state that the zoom button  210  is being depressed toward the wide-angle limit is detected, and a continuous zooming toward the life-size magnification is carried out for a time duration while the zoom button  210  is depressed. In this way, the photographer can vary the zoom ratio with use of the zoom button  210 , even if the subject is located away from the photographer. Similarly to ordinary life-size shooting, the photographer can capture an enlarged still image by moving the subject image within the display screen to an intended position, and by depressing the shutter button  204  with the subject image being located at the intended position.  
      Further, during the moving image shooting, the photographer can vary the zoom ratio of the subject image desirably by manipulating the zoom button  210 . Specifically, the moving image shooting is started in response to depressing of the shutter button  204  by the photographer. During the moving image shooting, the zoom ratio of the subject image can be arbitrarily changed by manipulating the zoom button  210 . When the photographer depresses the shutter button  402  again in this state, the moving image shooting is terminated.  
      The construction of the zoom button  210  in the camera phone  220  is not limited to the foregoing. The dial button  205  may be used as a zoom button. Alternatively, it is possible to use a member having two-directional zooming function, namely, enlargement and reduction, such as a rotary dial member which is rotatably supported about an axis of rotation on the operating face where the dial button is installed.  
      In the foregoing embodiment, the longer side Lt 1  of the display  202  and the longer side Lt 2  of the image sensor  105  are aligned parallel to each other in the vertical directions on the plane of  FIGS. 8A through 8C . Alternatively, it is possible to align the longer side Lt 1  of the display  202  and the longer side Lt 2  of the image sensor  105  parallel to each other in a certain direction, e.g., transverse directions, on the plane of  FIGS. 8A through 8C . Such an altered arrangement enables image display of maximally utilizing the display area of the display  202 , which contributes to effective confirmation of the image composition in image shooting.  
      The same idea as applied to the camera phones  200  and  220  is applied to various digital apparatuses incorporated with a display as a display device, such as a foldable camera phone, a digital still camera, a digital video camera, a PDA, a personal computer, a mobile computer, and peripheral devices thereof.  
       FIGS. 9A and 9B  are external schematic views each showing a foldable camera phone  300 .  FIG. 9A  shows an operating face of the camera phone  300 , and  FIG. 9B  shows a back face of the camera phone  300 . The camera phone  300  is of a foldable type, wherein a first casing  310  and a second casing  320  are coupled to each other by a hinge member  330 . A vertically elongated display  311  is provided on the operating face of the first casing  310 , and a key entering section  321  serving as an operating section is provided on the operating face of the second casing  320 .  
      The camera phone  300  is constructed in such a manner that a taking lens device  206  including an imaging optical system  100  or a zoom optical system  110 , and an image sensor  105  are arranged in the first casing  310 , and a taking lens element  207  of the taking lens device  206  is exposed out of the back face of the first casing  310 . Specifically, an incident surface of the taking lens device  206  for receiving an optical image of a subject and a display  311  are arranged on the back face and the operating face of the first casing  310 , respectively. With this arrangement, an image can be captured while the image acquired through the taking lens device  206  is displayed on the display  311 . The display  311  and the image sensor  105  are assembled in such a manner that a longer side Lt 1  of the display  311  and a longer side Lt 2  of the image sensor  105  are aligned parallel to each other in the same direction. Thereby, an optical image of a subject that has been incident through the taking lens element  207  and captured on a rectangular imaging area of the image sensor  105  can be effectively displayed on the rectangular display  311  in image shooting.  
       FIGS. 10A and 10B  are external schematic views of a PDA, wherein  FIG. 10A  shows an operating face of the PDA  400 , and  FIG. 10B  shows a back face thereof. A transversely elongated display  401 , and a key entering section  402  serving as an operating section are provided on the operating face of the PDA  400 .  
      The PDA  400  is constructed in such a manner that a taking lens device  206  including an imaging optical system  100  or a zoom optical system  110 , and an image sensor  105  are incorporated in a housing of the PDA  400 , with a taking lens element  207  of the taking lens device  206  being exposed out of the back face of the PDA  400 . Specifically, an incident surface of the taking lens device  206  for receiving an optical image of a subject and the display  401  are arranged on the back face and the operating face of the PDA  400 , respectively. With this arrangement, an image can be captured while the image acquired through the taking lens device  206  is displayed on the display  401 . The display  401  and the image sensor  105  are assembled in such a manner that a longer side Lt 1  of the display  401  and a longer side Lt 2  of the image sensor  105  are aligned parallel to each other in a certain direction, in this case, a horizontal direction. Thereby, an optical image of a subject that has been incident through the taking lens element  207  and captured on a rectangular imaging area of the image sensor  105  can be effectively displayed on the rectangular display  401  in image shooting.  
      Hereinafter, the terms “concave”, “convex”, and “meniscus” are used regarding lens elements. It should be noted that these terms represent the respective configurations of a lens element in the vicinity of the optical axis, namely, near the central part of the lens element, and do not indicate the respective configurations of the entirety of the lens element or a periphery of the lens element. As far as the lens element is spherical, the configuration of the lens element does not matter. However, since the configuration of an aspherical lens element is generally different in the vicinity of the central part thereof and in a periphery thereof, the above definitions on the terms are necessary. The aspherical lens element includes lens elements having surfaces of different configurations such as a paraboloidal surface, an ellipsoidal surface, a hyperboloidal surface, and a quartic surface.  
      Further, throughout the specification and the claims, the optical power of a single lens element and the optical power of each single lens element constituting a cemented lens element indicate a power of the single lens element itself assuming that both of the lens surfaces of the single lens element have a boundary with the air.  
     Description on Embodiments of Imaging Optical System  
      In the following, embodiments of the imaging optical system  100  as shown in  FIG. 1A , specifically, exemplified arrangements of the imaging optical system  100  constituting the imaging lens device  206  to be loaded in the camera phone  200  as shown in  FIGS. 8A and 8B , the camera phone  220  as shown in  FIG. 8C , the camera phone  300  as shown in  FIGS. 9A and 9B , or the portable digital assistant (PDA)  400  as shown in  FIGS. 10A and 10B  are described referring to the drawings.  
     First Embodiment  
       FIG. 11  is a cross-sectional view of an arrangement of an imaging optical system  51  as a first embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 11 . As shown in  FIG. 11 , the imaging optical system  51  has, from the object side along the optical path, a first reflecting prism  1  having a positive optical power as a whole, which corresponds to the incident side prism  101  shown in  FIG. 1A , an aperture stop (ST) for regulating the light amount, a first lens element  2  having a positive optical power, a second lens element  3  having a negative optical power, and a second reflecting prism  4  having a positive optical power as a whole, which corresponds to the imaging side prism  102  shown in  FIG. 1A . A plane parallel plate  5  and an image sensor  6  are arranged on the side of the second reflecting prism  4  opposite to the second lens element  3 .  
       FIG. 11 , as well as  FIGS. 14 and 16  respectively showing a second embodiment and a third embodiment of the invention, which will be described later, each shows an arrangement of optical devices with an infinite focal length.  FIGS. 12, 15 , and  17  are illustrations each showing an arrangement of an imaging optical system, wherein a lens element having a function substantially equivalent to the function of a reflecting prism such as a first reflecting prism and a second reflecting prism shown in  FIGS. 11, 14 , and  16  is used in place of the reflecting prism shown in  FIGS. 11, 14 , and  16 , respectively. The direction of the arrows D in  FIG. 12  ( 15  or  17 ) corresponds to the longer side direction of the image sensor  6 . The imaging optical systems shown in  FIGS. 11, 14 , and  16  each is an imaging optical system, wherein an incident ray is bent in the shorter side direction of the image sensor  6 . The optical power throughout the specification and the claims means a power in a condition that mediums on both surfaces of the lens element are the air. The image sensor  6  has an aspect ratio of 3:4, for instance, has a size of 1.8 mm in vertical direction and 2.4 mm in horizontal direction. The directions shown by the arrows A in  FIG. 11  correspond to the thickness direction of the camera phone shown in  FIGS. 8A through 8C .  
      Referring to  FIG. 11 , the first reflecting prism  1  has an incident surface la of a negative optical power, an exit surface  1   b  of a positive optical power, and a planar reflecting surface RL 1  arranged on the optical path between the incident surface  1   a  and the exit surface  1   b.  The second reflecting prism  4  has an incident surface  4   a  of a positive optical power, an exit surface  4   b  of a negative optical power, and a planar reflecting surface RL 2  arranged on the optical path between the incident surface  4   a  and the exit surface  4   b.  In this embodiment, the reflecting surface RL 1  formed on the first reflecting prism  1  and the reflecting surface RL 2  formed on the second reflecting prism  4  are each adapted to bend an incident ray at about 90 degrees to direct the reflected ray toward the first lens element  2  and the plane parallel plate  5 , respectively.  
      In this embodiment, whereas the first reflecting prism  1 , the second reflecting prism  4 , and the aperture stop (ST) are fixed, the first lens element  2  and the second lens element  3  are moved in the direction of the arrow B in  FIG. 11  in focusing a subject from an infinite focal point to a closest focal point.  
      The surface denoted by ri (i= 1 ,  2 ,  3 , . . . ) shown in  FIG. 12  indicates the i-th lens surface from the object side. In  FIG. 12 , the first lens element  2  is a bi-convex lens element, and the second lens element  3  is a negative meniscus lens element convex to the imaging side. In  FIG. 12 , elements corresponding to the first reflecting prism  1  and the second reflecting prism  4  shown in  FIG. 11  are depicted as a first reflecting prism  1 ′ and a second reflecting prism  4 ′, considering that the arrangement in  FIG. 12  uses lens elements having functions substantially equivalent to the functions of the first reflecting prism  1  and the second reflecting prism  4  in  FIG. 11 . The same definition is applied to the arrangements shown in  FIGS. 15 and 17 , which will be described below.  
      In the above construction, an incident ray from the object side or the subject side in  FIG. 11  is incident onto the incident surface la of the first reflecting prism  1 , bent at about 90 degrees on the reflecting surface RL 1 , and then incident onto the first lens element  2 , the second lens element  3 , and the incident surface  4   a  of the second reflecting prism  4  in this order. Subsequently, the incident ray is bent at about 90 degrees on the reflecting surface RL 2 , and goes out of the exit surface  4   b  for forming an optical image of the object. The optical image formed by these optical devices of the imaging optical system  51  propagates through the plane parallel plate  5  arranged in proximity to the second reflecting prism  4 . At this time, the optical image is corrected in such a manner that a so-called alias noise generated in converting the optical image signal into an electrical signal by the image sensor  6  is minimized. The plane parallel plate  5  corresponds to an optical low-pass filter, an infrared cut filter, a cover glass for the image sensor, or an equivalent element.  
      Lastly, the optical image corrected by the plane parallel plate  5  is converted into an electrical signal by the image sensor  6 . The electrical signal undergoes a predetermined digital image processing, an image compression processing or a like processing according to needs, and is recorded as a digital video signal into a memory device of the digital apparatus such as the camera phone  200  as shown in  FIGS. 8A and 8B , the camera phone  220  as shown in  FIG. 8C , the camera phone  300  as shown in  FIGS. 9A and 9B , or the PDA  400  as shown in  FIGS. 10A and 10B , or transmitted to another digital apparatus by a cable or wirelessly. Preferably, a cover glass is provided on the subject side relative to the incident surface  1   a  of the first reflecting prism  1  to keep the imaging optical system  51 , particularly, the first reflecting prism  1  from being smeared.  
      In the following, the lens arrangements of the second embodiment and the third embodiment are described in this order referring to the drawings, as in the case of the first embodiment. It should be noted that elements in  FIGS. 14 through 17  which are equivalent to those in  FIGS. 11 and 12  are denoted by the same reference numerals.  
     Second Embodiment  
       FIG. 14  is a cross-sectional view of an arrangement of an imaging optical system  52  as a second embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 14 . As shown in  FIG. 14 , the imaging optical system  52  has, from the object side along the optical path, an aperture stop (ST) for regulating the light amount, a first reflecting prism  7  having a positive optical power as a whole, a first lens element  8  having a negative optical power, and a second reflecting prism  9  having a positive optical power as a whole.  
      The first reflecting prism  7  has an incident surface  7   a  of a positive optical power, an exit surface  7   b  of a positive optical power, and a planar reflecting surface RL 3  arranged on the optical path between the incident surface  7   a  and the exit surface  7   b.  The second reflecting prism  9  has an incident surface  9   a  of a positive optical power, an exit surface  9   b  of a negative optical power, and a planar reflecting surface RL 4  arranged on the optical path between the incident surface  9   a  and the exit surface  9   b.    
      In this embodiment, whereas the aperture stop (ST), the first reflecting prism  7 , and the second reflecting prism  9  are fixed, the first lens element  8  is moved in the direction shown by the arrow C in  FIG. 14  in focusing a subject from an infinite focal point to a closest focal point. The first lens element  8  is a negative meniscus lens element convex to the imaging side.  
     Third Embodiment  
       FIG. 16  is a cross-sectional view of an arrangement of an imaging optical system  53  as a third embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 16 . As shown in  FIG. 16 , the imaging optical system  53  has, from the object side along the optical path, a first reflecting prism  10  having a positive optical power as a whole, an aperture stop (ST) for regulating the light amount, a first lens element  11  having a positive optical power, a second lens element  12  having a negative optical power, and a second reflecting prism  13  having a positive optical power as a whole.  
      The first reflecting prism  10  has an incident surface  10   a  of a negative optical power, an exit surface  10   b  of a positive optical power, and a planar reflecting surface RL 5  arranged on the optical path between the incident surface  10   a  and the exit surface  10   b.  The second reflecting prism  13  has an incident surface  13   a  of a negative optical power, an exit surface  13   b  of a positive optical power, and a planar reflecting surface RL 6  arranged on the optical path between the incident surface  13   a  and the exit surface  13   b.    
      In this embodiment, whereas the first reflecting prism  10 , the second reflecting prism  13 , and the aperture stop (ST) are fixed, the first lens element  11  and the second lens element  12  are moved in the direction of the arrow B in  FIG. 16  in focusing a subject from an infinite focal point to a closest focal point. The first lens element  11  is a biconvex lens element having a positive optical power, and the second lens element  12  is a negative meniscus lens element convex to the imaging side. The first lens element  11  and the second lens element  12  are cemented together.  
      As mentioned above in each of the first through the third embodiments, the imaging optical system  51  ( 52  or  53 ) is constructed in such a manner that the two reflecting prisms each adapted to bend an incident ray at about 90 degrees for reflection are arranged in a state that the incident surface of the reflecting prism disposed on the subject side along the optical path and the exit surface of the other reflecting prism are aligned substantially parallel to each other. This arrangement contributes to miniaturization of the imaging optical system.  
      Specifically, as shown in  FIG. 12 , for instance, if an imaging optical system  501  corresponding to the imaging optical system  51  shown in  FIG. 11  is constructed without a reflecting prism, namely, without forming a reflecting surface for bending an incident ray at about 90 degrees for reflection, and the imaging optical system  501  is loaded in a camera phone corresponding to the camera phone  200  or the like, then, the thickness of the camera phone in the direction of the arrows B in  FIG. 12 , which corresponds to the thickness direction of the camera phone  200  shown in  FIGS. 8A and 8B , is equal to or larger than the entire length of the imaging optical system  501 . As a result, the thickness of the camera phone may be unduly increased, and the size of the camera phone  200  may be increased as a whole.  
      In view of the above, there may be proposed an arrangement of an imaging optical system  502  having one reflecting surface, as shown in  FIG. 13 . In this arrangement, a first reflecting prism  1  is provided in place of the lens element  1 ′ shown in  FIG. 12 . This arrangement may be advantageous in decreasing the thickness of the camera phone in the direction of the arrows A, which partly contributes to miniaturization of the camera phone, as compared with the arrangement shown in  FIG. 12 .  
      It should be noted, however, that the image sensor  6  is equipped with a packaging unit and an electrical wiring, and has a large size in the direction parallel with the light receiving surface of the image sensor  6  due to this arrangement. Therefore, the thickness of the camera phone is equal to or larger than the size of the image sensor  6  in the direction parallel with the light receiving surface, namely, is equal to or larger than the length L shown in  FIG. 13 . Thus, the arrangement as shown in  FIG. 13  does not sufficiently contribute to miniaturization of the camera phone.  
      In view of the above, in the embodiment of the invention as shown in  FIG. 11 , the imaging optical system  51  provided with the two reflecting surfaces, namely, the first reflecting prism  1  and the second reflecting prism  4 , in place of the lens elements  1 ′ and  4 ′ shown in  FIG. 12 , enables to miniaturize the camera phone  200  in the thickness direction thereof in light of the fact that the thickness direction of the imaging optical system  51  corresponds to the widthwise direction L′(&lt;L) of the first reflecting prism  1  shown by the arrows A.  
      In the following, the imaging optical systems  51 ,  52 , and  53  as the first through the third embodiments are described in detail referring to construction data, aberration diagrams and the like.  
     PRACTICAL EXAMPLES  
     Example 1  
      Construction data on the respective lens elements in the imaging optical system  51  as the first embodiment (Example 1) are described in Tables 1 and 2. It should be noted that the second reflecting prism corresponding to the imaging side prism is made of a plastic material, and the optical devices other than the second reflecting prism are made of glass in Examples 1 through 3.  
                           TABLE 1                                      AXIAL DISTANCE               BETWEEN           SURFACES                                     LENS   RADIUS   INFINITE   CLOSEST   REFRAC-           SURFACE   OF CUR-   FOCAL   FOCAL   TIVE   ABBE       No.   VATURE   POINT   POINT   INDEX   NUMBER                                             OBJECT   ∞   ∞   500   1.53048   55.72       r1*   −5.774   5.072       r2*   −4.181   1.000       r3   ∞   1.880   1.483       r4*   4.406   1.300       1.53048   55.72       r5*   5.943   0.256       r6*   −2.481   1.300       1.58340   30.23       r7*   −37.890   1.764   2.177       r8*   6.091   4.581       1.53048   55.72       r9*   12.992   0.268       r10   ∞   0.300   1.51680   65.26       r11   ∞   0.500       r12   ∞                  
 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
               
               
                 ASPHER- 
                   
                   
                   
                   
                   
               
               
                 ICAL 
                   
                   
                   
                   
                   
               
               
                 SUR- 
                   
                   
                   
                   
                   
               
               
                 FACE 
                 K 
                 A4 
                 A6 
                 A8 
                 A10 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 0 
                 1.853E−03 
                 −1.433E−05 
                 −3.034E−06 
                 1.441E−07 
               
               
                 2 
                 0 
                 0.709E−03 
                 −2.834E−04 
                 2.061E−05 
                 −3.885E−07 
               
               
                 4 
                 0 
                 1.190E−02 
                 −8.105E−04 
                 −1.480E−04 
                 2.893E−05 
               
               
                 5 
                 0 
                 1.226E−02 
                 1.226E−03 
                 −2.531E−03 
                 4.682E−04 
               
               
                 6 
                 0 
                 3.977E−02 
                 −3.632E−04 
                 −1.855−03 
                 4.047E−04 
               
               
                 7 
                 0 
                 2.062E−02 
                 6.115E−04 
                 2.407E−04 
                 −8.737E−06 
               
               
                 8 
                 0 
                 −3.634E−03 
                 2.999E−04 
                 −7.055E−04 
                 −5.445E−08 
               
               
                 9 
                 0 
                 1.913E−03 
                 −1.114E−03 
                 1.113E−04 
                 −3.456E−06 
               
               
                   
               
            
           
         
       
     
      Table 1 indicates, from the left-side column thereof, the respective lens surface numbers, radii of curvature (unit: mm) of the respective lens surfaces, distances (unit: mm) between the respective lens surfaces in the optical axis direction, namely, axial distances between the respective lens surfaces at the infinite focal point and the closest focal point, refractive indices of the respective lens elements, and the Abbe numbers of the respective lens elements. The axial distances are distances calculated on the presumption that the medium residing in the region between a pair of opposing planes including an optical plane and an imaging plane is the air. The value in each blank column regarding the axial distance between the lens surfaces at the closest focal point is the same as that in the corresponding left-side column at the infinite focal point. As shown in  FIG. 12 , the surface denoted by ri (i= 1 ,  2 ,  3 , . . . ) indicates the i-th lens surface from the object side on the optical path, and the surface ri marked with an asterisk (*) is an aspherical surface, namely, a refractive optical plane of an aspherical configuration or a plane having a refractive power substantially equivalent to the action of an aspherical plane in an optical path diagram substantially equivalent to the optical path diagram shown in  FIG. 11 .  
      Further, in Table 2, K represents a conical coefficient, and A 4 , A 6 , A 8 , and A 10  respectively represent aspheric coefficients of 4th, 6th, 8th, and 10th orders.  
      Further, since the aperture stop (ST), both sides of the plane parallel plate  5 , and the light receiving surface of the image sensor  6  are flat, respective radii of curvature thereof are infinite (∞).  
      The aspherical configuration of the lens surface is defined by the following conditional formula (3), wherein the apex of the lens surface is represented as the point of origin, and a local orthogonal coordinate system (x, y, z), with the direction from the object toward the image sensor being the positive z-axis direction is used.  
             z   =         c   ·     h   2         1   +       1   -       (     1   +   k     )     ⁢       c   2     ·     h   2                 +     A   ·     h   4       +     B   ·     h   6       +     C   ·     h   8       +     D   ·     h   10                 (   3   )             
 
 where 
      z represents a z-axis displacement at the height position h relative to the apex of the lens surface,     h represents a height in a direction perpendicular to the z-axis (h 2 =x 2 +y 2 ),     c represents a curvature near the apex of the lens surface (=1/radius of curvature),     A, B, C, and D respectively represent aspheric coefficients of 4th, 6th, 8th, and 10th orders, and     k represents a conical coefficient. As is obvious from the conditional formula (3), the radii of curvature of the respective aspheric lens elements in Table 1 each show a value approximate to the center of the corresponding lens element.    

      The spherical aberration (LONGITUDINAL SPHERICAL ABERRATION in  FIGS. 18A and 18D ), the astigmatism (ASTIGMATISM in  FIGS. 18B and 18E ), and the distortion aberration (DISTORTION in  FIGS. 18C and 18F ) of the optical system in Example 1 having the above lens arrangement and construction are shown in  FIGS. 18A through 18F . Specifically, the respective aberrations at the infinite focal point and the closest focal point are shown in the upper row and the lower row in  FIGS. 18A through 18F . Each of the horizontal axes in the spherical aberration diagrams shows a focal point displacement in the unit of mm. Each of the horizontal axes in the distortion aberration diagrams shows a distortion in terms of percentage. Each of the vertical axes in the spherical aberration diagrams shows a value standardized by the incident height, and each of the vertical axes in the astigmatism diagrams and the distortion aberration diagrams shows a height of an optical image or an image height in the unit of mm.  
      In the spherical aberration diagrams, aberrations in case of using light of three different wavelengths are shown, wherein the broken lines represent aberrations in a red ray (wavelength: 656.28 nm), the solid lines represent aberrations in a yellow ray (so-called “d-ray” having a wavelength of 587.56 nm), and the two-dotted-chain lines represent aberrations in a blue ray (wavelength: 435.84 nm). In the astigmatism diagrams, the dashed lines “T” and the solid lines “S” respectively represent displacements (unit: mm, represented by the horizontal axes) of a tangential (meridional) plane and a sagittal (radial) plane near the apex of the lens surface in the direction of the optical axis (AX). Further, the astigmatism diagrams and the distortion aberration diagrams show results of using the yellow ray or d-ray.  
      As is obvious from  FIGS. 18A through 18F , the imaging optical system  51  in Example  1  exhibits superior optical characteristics, wherein the spherical aberration, the astigmatism, and the distortion aberration are significantly small both at the infinite focal point and the closest focal point. The focal length (unit: mm), the F-number, and the maximum image height at the infinite focal point in Example 1 are shown in Table 7. Table 7 shows that Example 1 provides a fast optical system.  
     Example 2  
      Construction data on the respective lens elements in the imaging optical system  52  as the second embodiment (Example 2) are described in Tables 3 and 4.  
                           TABLE 1                                      AXIAL DISTANCE               BETWEEN           SURFACES                                     LENS   RADIUS   INFINITE   CLOSEST   REFRAC-           SURFACE   OF CUR-   FOCAL   FOCAL   TIVE   ABBE       No.   VATURE   POINT   POINT   INDEX   NUMBER                                             OBJECT   ∞   ∞   200               r1   ∞   0.000       r2*   17.833   4.371       1.58913   61.11       r3*   −2.135   0.482   0.544       r4*   −1.399   0.176       1.58340   30.23       r5*   −14.772   1.722   1.660       r6*   2.535   6.387       1.53048   55.72       r7*   47.000   0.205       r8   ∞   0.533       1.51680   65.26       r9   ∞   0.280       r10   ∞                  
 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 Table 4 
               
               
                   
               
               
                   
               
               
                 ASPHERICAL 
                   
                   
                   
                   
                   
                   
               
               
                 SURFACE 
                 K 
                 A4 
                 A6 
                 A8 
                 A10 
                 A12 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 2 
                 −314.18159 
                 3.075E−03 
                 4.414E−03 
                 −8.388E−03 
                 4.074E−03 
                   
               
               
                 3 
                 −3.774837 
                 −8.217E−03 
                 −8.113E−03 
                 1.411E−03 
                 5.197E−03 
               
               
                 4 
                 −3.207117 
                 −8.561E−02 
                 2.689E−03 
                 −1.388E−03 
                 −1.366E−03 
                 1.940E−04 
               
               
                 5 
                 39.078736 
                 −4.528E−02 
                 8.458E−03 
                 −8.667E−04 
                 3.170E−05 
                 4.181E−07 
               
               
                 6 
                 −4.108197 
                 2.180E−03 
                 −6.884E−04 
                 6.605E−05 
                 −4.774E−06 
                 1.244E−07 
               
               
                 7 
                 −1.47498E+27 
                 6.684E−03 
                 1.328E−04 
                 −1.663E−04 
                 1.858E−05 
                 −5.905E−07 
               
               
                   
               
            
           
         
       
     
      Similarly to Table 2, in Table 4, K represents a conical coefficient, and A 4 , A 6 , A 8 , A 10 , and A 12  respectively represent aspheric coefficients of 4th, 6th, 8th, 10th, and  12 th orders.  
     Example 3  
      Further, construction data on the respective lens elements in the imaging optical system  53  as the third embodiment (Example 3) are described in Tables 5 and 6.  
                           TABLE 1                                      AXIAL DISTANCE               BETWEEN           SURFACES                                     LENS   RADIUS   INFINITE   CLOSEST   REFRAC-           SURFACE   OF CUR-   FOCAL   FOCAL   TIVE   ABBE       No.   VATURE   POINT   POINT   INDEX   NUMBER               OBJECT   ∞   ∞   500               r1*   −5.168   4.939       1.58340   30.23       r2*   −5193.156   0.100       r3   ∞   0.822   0.743       r4*   2.852   3.000       1.53048   55.72       r5   2.753   0.240       1.58340   30.23       r6*   −16.022   3.073   3.171       r7*   −15.591   5.003       1.58340   30.23       r8*   −54.952   0.100       r9   ∞   0.300       1.51680   65.26       r10   ∞   0.282       r11   ∞                  
 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 6 
               
               
                   
               
               
                   
               
               
                 ASPHERICAL 
                   
                   
                   
                   
                   
               
               
                 SURFACE 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 −0.482825 
                 2.38E−03 
                 −1.83E−04 
                 3.60E−06 
                 −3.04E−06 
               
               
                 2 
                 −0.87E+36 
                 −7.35E−03 
                 2.77E−04 
                 3.51E−04 
                 −7.26E−05 
               
               
                 4 
                 −2.399317 
                 4.51E−04 
                 1.94E−04 
                 1.46E−06 
                 −6.10E−06 
               
               
                 6 
                 5.340723 
                 −1.91E−03 
                 −2.39E−04 
                 −1.12E−06 
                 −2.36E−07 
               
               
                 7 
                 48.069031 
                 −9.07E−03 
                 −1.22E−04 
                 −2.87E−06 
                 −2.77E−05 
               
               
                 8 
                 −4.09E+25 
                 −3.52E−03 
                 −7.01E−04 
                 1.23E−04 
                 −6.10E−06 
               
               
                   
               
            
           
         
       
     
       FIGS. 19A through 19F  are aberration diagrams of Example 2, and  FIGS. 20A through 20F  are aberration diagrams of Example 3. Specifically, the sperical aberration (LONGITUDINAL SPHERICAL ABERRATION in  FIGS. 19A, 19D ,  20 A, and  20 D), the astigmatism (ASTIGMATISM in  FIGS. 19B, 19E ,  20 B, and  20 E), and the distortion aberration (DISTORTION in  FIGS. 19C, 19F ,  20 C, and  20 F) of the optical systems in Examples 2 and 3 are shown in  FIGS. 19A through 20F . As is obvious from  FIGS. 19A through 20F , the imaging optical systems  52  and  53  in Examples 1 and 2 exhibit superior optical characteristics, wherein the spherical aberration, the astigmatism, and the distortion aberration are significantly small both at the infinite focal point and the closest focal point. The focal length (unit: mm) and the F-number at the infinite focal point in Examples 2 and 3 are shown in Table 7, as well as Example 1. Table 7 shows that Examples 2 and 3 each provide a fast optical system, as well as Example 1.  
                               TABLE 7                                      FOCAL LENGTH   F   MAXIMUM IMAGE           (mm)   NUMBER   HEIGHT (mm)                                         EXAMPLE 1   6.82   3.5   3       EXAMPLE 2   6.4   3.6   3       EXAMPLE 3   6.4   3   3                    
      The arrangement relation between the second prism  4  ( 9  or  13 ) and the image sensor  6  in Examples 1 through 3 is defined as shown in Table 8 to miniaturize the imaging optical system  51  ( 52  or  53 ). Specifically, the height a (unit: mm) of the light receiving surface of the image sensor  6  on the plane where the optical path of the image sensor  6  is folded, which corresponds to the plane of  FIG. 11  ( FIG. 14  or  FIG. 16 ), the distance d (unit: mm) between the exit surface  4   b  ( 9   b  or  13   b ) of the second reflecting prism  4  ( 9  or  13 ) and the light receiving surface of the image sensor  6 , and the respective calculation results of the conditional formula (1) in Examples 1 through 3 are as shown in Table 8.  
                               TABLE 8                                      HEIGHT (a) OF LIGHT RECEIVING   DISTANCE (d) BETWEEN EXIT               SURFACE OF IMAGE SENSOR   SURFACE OF SECOND REFLECTING           ON PLANE WHERE OPTICAL   PRISM AND LIGHT RECEIVING           PATH IS FOLDED   SURFACE OF IMAGE SENSOR   d/a                                         EXAMPLE 1   3.600   1.052   0.292       EXAMPLE 2   3.600   1.018   0.283       EXAMPLE 3   3.600   0.682   0.189                  
 
      Further, in Examples 1 through 3, the second reflecting prisms  4 ,  9 , and  13  respectively satisfying the parameters as shown in Table 9 are adopted to optimize the size or the length of the second reflecting prisms  4 ,  9  and  13 . Specifically, the refractive index n of the second reflecting prism  4  ( 9  or  13 ), the distance t of the principal ray, the exit pupil distance p, and the respective calculation results of the conditional formula (2) in Examples 1 through 3 are as shown in Table 9, wherein the units of the parameters t and p are mm.  
                           TABLE 9                                      DISTANCE               (t) OF                                     REFRACTIVE   PRINCIPAL   EXIT PUPIL               INDEX (n)   RAY   DISTANCE (p)   (t · n)/p                                             EXAMPLE 1   1.530   4.581   −8.473   −0.827       EXAMPLE 2   1.530   6.387   −22.690   −0.431       EXAMPLE 3   1.583   5.003   −9.387   −0.844                  
 
      The imaging optical systems  51 ,  52 , and  53  in Examples 1 through 3 adopt the parameters as shown in Tables 8 and 9. This arrangement enables to reduce the size of the imaging optical system  51  ( 52  or  53 ) in the thickness direction thereof corresponding to the direction of the arrows L′ in  FIG. 11 , which securely contributes to miniaturization of the digital apparatus in the thickness direction thereof.  
     Description on Embodiments of Zoom Optical System  
      Next, embodiments of the zoom optical system  110  as shown in  FIG. 7 , specifically, exemplified arrangements of the zoom optical system  110  constituting the imaging lens device  206  to be loaded in the camera phone  200  as shown in  FIGS. 8A and 8B , the camera phone  220  as shown in  FIG. 8C , the camera phone  300  as shown in  FIGS. 9A and 9B , or in the PDA  400  as shown in  FIGS. 10A and 10B  are described referring to the drawings.  
     Fourth Embodiment  
       FIG. 21  is a cross-sectional view of an arrangement of a zoom optical system  54  as a fourth embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 21 .  FIG. 21  shows an arrangement of optical devices of the zoom optical system  54  with an infinite focal length.  FIG. 21 , as well as  FIGS. 22 through 27  each schematically show an optical path along which an incident ray from the object side propagates, with its axis serving as the optical axis (AX).  
      The zoom optical system  54  comprises, from the object side along the optical path, a first lens group (Gr 1 ) including a first reflecting prism (PR 1 ), which corresponds to the incident side prism  101  in  FIG. 7 , and has a negative optical power as a whole; a second lens group (Gr 2 ) having a negative optical power as a whole and including a cemented lens element consisting of a biconcave lens element (L 1 ) having a negative optical power and a biconvex lens element (L 2 ) having a positive optical power; a third lens group (Gr 3 ) including an aperture stop (ST), having a positive optical power as a whole, and including a cemented lens element consisting of a negative meniscus lens element (L 3 ) convex to the imaging side and a biconvex positive lens element (L 4 ), and a positive meniscus lens element (L 5 ) convex to the object side; and a fourth lens group (Gr 4 ) having a second reflecting prism (PR 2 ), which corresponds to the imaging side prism  102  in  FIG. 7 , and has a positive optical power. The optical axes of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are designed to be aligned with the axis (AX) of the optical path between the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ). A plane parallel plate (PL) and an image sensor (SR) are arranged on the imaging side of the second reflecting prism (PR 2 ). The image sensor (SR) has an aspect ratio of 3:4, for instance.  
      Further, the first reflecting prism (PR 1 ) has an incident surface (S 1 ) of a negative optical power, an exit surface (S 3 ) of a positive optical power, and a planar reflecting surface (S 2 ) arranged on the optical path between the incident surface (S 1 ) and the exit surface (S 3 ). The second reflecting prism (PR 2 ) has an incident surface (S 4 ) of a positive optical power, an exit surface (S 6 ) of a negative optical power, and a planar reflecting surface (S 5 ) arranged on the optical path between the incident surface (S 4 ) and the exit surface (S 6 ). In this embodiment, the reflecting surface (S 2 ) formed on the first reflecting prism (PR 1 ) and the reflecting surface (S 5 ) formed on the second reflecting prism (PR 2 ) are adapted to bend an incident ray at about 90 degrees to direct the reflected ray toward the second lens group (Gr 2 ) and the plane parallel plate (PL), respectively.  
      The zoom optical system  54  shown in  FIG. 21  is a zoom optical system in which an incident ray is bent in the shorter side direction of the image sensor (SR). In other words, transverse directions in  FIG. 21  correspond to the shorter side direction of the image sensor (SR), and the direction of the arrows A corresponds to the thickness direction of the camera phone  200  as shown in  FIGS. 8A and 8B  or the camera phone  220  as shown in  FIG. 8C .  
       FIG. 22  is an illustration showing a zoom optical system equivalent to the zoom optical system  54  in  FIG. 21 , wherein lens elements (LP 1 , LP 2 ) having functions substantially equivalent to the functions of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 21  are used in place of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 21 . The surface denoted by ri (i= 1 ,  2 ,  3 , . . . ) in  FIG. 22  indicates the i-th lens surface from the object side, and the surface ri marked with an asterisk (*) is an aspherical surface. The direction of the arrows D in  FIG. 22  corresponds to the longer side direction of the image sensor (SR).  
      The number of the lens elements constituting the cemented lens element is not the number of the cemented lens element itself but is the number of single lens elements constituting the cemented lens element. For instance, if the cemented lens element is constituted of three single lens elements, the number of the lens elements constituting the cemented lens element is three.  
      In the above construction, an incident ray from the object side or the subject side in  FIG. 21  is incident onto the incident surface (S 1 ) of the first reflecting prism (PR 1 ), bent at about 90 degrees on the reflecting surface (S 2 ), and goes out of the exit surface (S 3 ). Then, the exit ray propagates through the second lens group (Gr 2 ) and the third lens group (Gr 3 ), and is incident onto the incident surface (S 4 ) of the second reflecting prism (PR 2 ). Then, the incident ray is bent at about 90 degrees on the reflecting surface (S 5 ), and goes out of the exit surface (S 6 ) for forming an optical image of an object. The optical image propagates through the plane parallel plate (PL) arranged in proximity to the second reflecting prism (PR 2 ). At this time, the optical image is corrected in such a manner that a so-called alias noise generated in converting the optical image signal into an electrical signal by the image sensor (SR) is minimized. The plane parallel plate (PL) corresponds to an optical low-pass filter, an infrared cut filter, a cover glass for the image sensor, or an equivalent element.  
      Lastly, the optical image corrected by the plane parallel plate (PL) is converted into an electrical signal by the image sensor (SR). The electrical signal undergoes a predetermined digital image processing, an image compression processing or a like processing according to needs, and is recorded, as a digital video signal, into a memory device of the digital apparatus such as the camera phone  200  as shown in  FIGS. 8A and 8B , the camera phone  220  as shown in  FIG. 8C , the camera phone  300  as shown in  FIGS. 9A and 9B , or the PDA  400  as shown in  FIGS. 10A and 10B , or transmitted to another digital apparatus by a cable or wirelessly.  
      Hereinafter, an intermediate point between the wide angle limit (W) where the focal length is the shortest, namely, the angle of view is the largest, and the telephoto limit (W) where the focal length is the longest, namely, the angle of view is the smallest is called as “mid point (M)”.  
      In the lens arrangement of the fourth embodiment as shown in  FIG. 21 , the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) are fixed, the second lens group (Gr 2 ) makes a U-turn in such a manner that the second lens group (Gr 2 ) comes closest to the imaging side around the mid point (M), and the third lens group (Gr 3 ) is substantially linearly moved toward the object side during zooming from the wide angle limit (W) to the telephoto limit (T) as shown in  FIG. 22 . At this time, both the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are moved in the optical axis direction of the lens groups for zooming. It should be noted that the moving direction, the moving amount, and other parameter of the lens groups are changeable depending on the optical power of the lens groups or the like.  
      It is desirable to fix the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) and move at least one of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) in parallel to the optical axis, namely, in the direction of the arrows B in  FIG. 21  in focusing a subject from an infinite focal point to a closest focal point. This arrangement enables focusing without changing the thickness of the entirety of the zoom optical system  54  in the direction of the arrows A in  FIG. 21 .  
      In the following, as in the case of the fourth embodiment, the lens arrangements of the fifth embodiment and the sixth embodiment are described in this order referring to the drawings. Elements in  FIGS. 23 and 25  equivalent to those in  FIG. 21  are denoted by the same references, and elements in  FIGS. 24 and 26  equivalent to those in  FIG. 22  are denoted by the same reference numerals. It should be noted, however, that the elements of the like reference numerals are not necessarily identical to each other. For instance, although the first reflecting prisms in  FIGS. 21, 23 , and  25  are denoted by the same reference numeral (PR 1 ), this does not mean that the first reflecting prisms in  FIGS. 21, 23 , and  25  are identical to each other.  
     Fifth Embodiment  
       FIG. 23  is a cross-sectional view of an arrangement of a zoom optical system  55  as the fifth embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 23 .  FIG. 23  shows an arrangement of optical devices with an infinite focal length.  
      The zoom optical system  55  comprises, from the object side along the optical path, a first lens group (Gr 1 ) including a first reflecting prism (PR 1 ) having a negative optical power, and a cemented lens element having a negative optical power as a whole and consisting of a biconcave negative lens element (L 1 ) and a biconvex positive lens element (L 2 ); a second lens group (Gr 2 ) including an aperture stop (ST), having a negative optical power as a whole, and including a cemented lens element consisting of a negative meniscus lens element (L 3 ) convex to the object side and a biconvex positive lens element (L 4 ); a third lens group (Gr 3 ) having a positive meniscus lens element (L 5 ) convex to the object side; and a fourth lens group (Gr 4 ) having a second reflecting prism (PR 2 ) of a positive optical power. The optical axes of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are designed to be aligned with the axis (AX) of the optical path between the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ). A plane parallel plate (PL) and an image sensor (SR) are arranged on the imaging side of the second reflecting prism (PR 2 ).  
      Further, the first reflecting prism (PR 1 ) has an incident surface (S 1 ) of a negative optical power, an exit surface (S 3 ) of a positive optical power, and a planar reflecting surface (S 2 ) arranged on the optical path between the incident surface (S 1 ) and the exit surface (S 3 ). The second reflecting prism (PR 2 ) has an incident surface (S 4 ) and an exit surface (S 6 ) both having a positive optical power, and a planar reflecting surface (S 5 ) arranged on the optical path between the incident surface (S 4 ) and the exit surface (S 6 ). In this embodiment, the reflecting surface (S 2 ) formed on the first reflecting prism (PR 1 ) and the reflecting surface (S 5 ) formed on the second reflecting prism (PR 2 ) are adapted to bend an incident ray at about 90 degrees to direct the reflected ray toward the second lens group (Gr 2 ) and the plane parallel plate (PL), respectively.  
      The zoom optical system  55  shown in  FIG. 23  is a zoom optical system in which an incident ray is bent in the shorter side direction of the image sensor (SR), as in the case of  FIG. 21 . The direction of the arrows A in  FIG. 23  corresponds to the thickness direction of the camera phone  200  as shown in  FIGS. 8A and 8B  or the camera phone  220  as shown in  FIG. 8C .  
       FIG. 24  is an illustration showing a zoom optical system equivalent to the zoom optical system  55  in  FIG. 23 , wherein lens elements having functions substantially equivalent to the functions of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 23  are used in place of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 23 . The direction of the arrows D in  FIG. 24  corresponds to the longer side direction of the image sensor (SR).  
      In the above construction, an incident ray from the object side in  FIG. 23  is bent on the reflecting surface (S 2 ) of the first reflecting prism (PR 1 ) at about 90 degrees, propagates through the second lens group (Gr 2 ) and the third lens group (Gr 3 ), and is bent on the reflecting surface (S 5 ) of the second reflecting prism (PR 2 ) at about 90 degrees for forming an optical image of a subject onto the light receiving surface of the image sensor (SR).  
      In the lens arrangement of the fifth embodiment as shown in  FIG. 23 , the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) are fixed, the second lens group (Gr 2 ) is substantially linearly moved toward the object side, and the third lens group (Gr 3 ) is also moved toward the object side with its distance to the second lens group (Gr 2 ) being changed during zooming from the wide angle limit (W) to the telephoto limit (T) as shown in  FIG. 24 . At this time, both the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are moved in the optical axis direction of the lens groups for zooming.  
      It is desirable to fix the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ), and to move at least one of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) in parallel to the optical axis, namely, in the direction of the arrows B in  FIG. 23  in focusing a subject from an infinite focal point to a closest focal point. This arrangement enables focusing without changing the thickness of the entirety of the zoom optical system  55  in the direction of the arrows A in  FIG. 23 .  
     Sixth Embodiment  
       FIG. 25  is a cross-sectional view of an arrangement of a zoom optical system  56  as the sixth embodiment taken along a longitudinal direction of the optical axis (AX) in  FIG. 25 .  FIG. 25  shows an arrangement of optical devices with an infinite focal length.  
      The zoom optical system  56  comprises, from the object side along the optical path, a first lens group (Gr 1 ) having a negative optical power as a whole, and including a first reflecting prism (PR 1 ), and a cemented lens element consisting of a biconcave negative lens element (L 1 ) and a biconvex positive lens element (L 2 ); a second lens group (Gr 2 ) having a positive optical power as a whole, and including an aperture stop (ST), and a cemented lens element consisting of a negative meniscus lens element (L 3 ) convex to the object side and a biconvex positive lens element (L 4 ); a third lens group (Gr 3 ) having a positive meniscus lens element (L 5 ) convex to the object side; and a fourth lens group (Gr 4 ) including a second reflecting prism (PR 2 ) of a negative optical power. The optical axes of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are designed to be aligned with the axis (AX) of the optical path between the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ). A plane parallel plate (PL) and an image sensor (SR) are arranged on the imaging side of the second reflecting prism (PR 2 ).  
      Further, the first reflecting prism (PR 1 ) has an incident surface (S 1 ) of a negative optical power, an exit surface (S 3 ) of a positive optical power, and a planar reflecting surface (S 2 ) arranged on the optical path between the incident surface (S 1 ) and the exit surface (S 3 ). The second reflecting prism (PR 2 ) has an incident surface (S 4 ) of a positive optical power, an exit surface (S 6 ) of a negative optical power, and a planar reflecting surface (S 5 ) arranged on the optical path between the incident surface (S 4 ) and the exit surface (S 6 ). In this embodiment, the reflecting surface (S 2 ) formed on the first reflecting prism (PR 1 ) and the reflecting surface (S 5 ) formed on the second reflecting prism (PR 2 ) are adapted to bend an incident ray at about 90 degrees to direct the reflected ray toward the second lens group (Gr 2 ) and the plane parallel plate (PL), respectively.  
      The zoom optical system  56  shown in  FIG. 25  is a zoom optical system in which an incident ray is bent in the shorter side direction of the image sensor (SR), as in the cases of  FIGS. 21 and 23 . The direction of the arrows A corresponds to the thickness direction of the camera phone  200  as shown in  FIGS. 8A and 8B  or the camera phone  220  as shown in  FIG. 8C .  
       FIG. 26  is an illustration showing a zoom optical system equivalent to the zoom optical system  56  in  FIG. 25 , wherein lens elements having functions substantially equivalent to the functions of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 25  are used in place of the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) in  FIG. 25 . The direction of the arrows D in  FIG. 26  corresponds to the longer side direction of the image sensor (SR).  
      In the above construction, an incident ray from the object side in  FIG. 25  is bent on the reflecting surface (S 2 ) of the first reflecting prism (PR 1 ) at about 90 degrees, propagates through the second lens group (Gr 2 ) and the third lens group (Gr 3 ), and is bent on the reflecting surface (S 5 ) of the second reflecting prism (PR 2 ) at about 90 degrees for forming an optical image of a subject onto the light receiving surface of the image sensor (SR).  
      In the lens arrangement of the sixth embodiment as shown in  FIG. 25 , the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) are fixed, the second lens group (Gr 2 ) is moved toward the object side, and the third lens group (Gr 3 ) is also moved toward the object side with its distance to the second lens group (Gr 2 ) being changed during zooming from the wide angle limit (W) to the telephoto limit (T) as shown in  FIG. 26 . At this time, both the second lens group (Gr 2 ) and the third lens group (Gr 3 ) are moved in the optical axis direction of the lens groups for zooming.  
      It is desirable to fix the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ), and to move at least one of the second lens group (Gr 2 ) and the third lens group (Gr 3 ) in parallel to the optical axis, namely, in the direction of the arrows B in  FIG. 25  in focusing a subject from an infinite focal point to a closest focal point. This arrangement enables focusing without changing the thickness of the entirety of the zoom optical system  56  in the direction of the arrows A in  FIG. 25 .  
      In the fourth to the sixth embodiments as described above, as in the case of the first through the third embodiments, preferably, a cover glass may be provided on the subject side relative to the incident surface of the first reflecting prism  1  to keep the zoom optical system, particularly, the first reflecting prism (PR 1 ) from being smeared. Since the thickness of the cover glass is generally small, there is no or less likelihood that providing the cover glass may unduly increase the thickness of the entirety of the optical system.  
      In the following, the zoom optical systems  54 ,  55 , and  56  as the fourth through the sixth embodiments are described in detail referring to construction data, aberration diagrams and the like.  
     PRACTICAL EXAMPLES  
     Example 4  
      Construction data on the respective lens elements in the zoom optical system  54  as the fourth embodiment (Example 4) are described in Tables 10 and 11. It should be noted that the second reflecting prism corresponding to the imaging side prism is made of a plastic material, and the optical devices other than the second reflecting prism are made of glass in Examples 4 through 6.  
                               TABLE 10                                  AXIAL DISTANCE               LENS       BETWEEN SUR-               SUR-   RADIUS OF   FACES (INFINITE   REFRAC-   ABBE       FACE   CURVATURE   FOCAL POINT, mm)   TIVE   NUM-                                         No.   (mm)   W   M   T   INDEX   BER               OBJECT   —   ∞   ∞   ∞               r1*   −8.591   7.181           1.58340   30.23       r2*   −16.102   1.019   1.826   0.656       r3   −5.670   0.574           1.67603   54.67       r4   5.934   0.008           1.51400   42.83       r5   5.934   1.336           1.84828   33.62       r6   −41.351   5.462   1.713   0.100       r7       0.574       r8   8.031   3.400           1.84666   23.82       r9   3.690   0.008           1.51400   42.83       r10   3.690   1.488           1.64275   56.36       r11   −89.291   0.100       r12*   3.741   3.393           1.51342   66.94       r13*   4.610   1.076   3.861   6.645       r14*   11.242   6.468           1.51680   64.20       r15*   −25.187   0.483       r16   ∞   0.500           1.51680   64.20       r17   ∞   0.500       r18   ∞                  
 
     
       
         
           
               
               
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                   
               
               
                 LENS SURFACE 
                 CONICAL 
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 No. 
                 COEFFICIENT 
                 A 
                 B 
                 C 
                 D 
                 E 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 r1* 
                 0.098636 
                 1.39E−03 
                 −3.05E−05 
                 1.65E−06 
                 −5.70E−08 
                 8.64E−10 
               
               
                 r2* 
                 0 
                 7.89E−04 
                 −5.99E−05 
                 8.21E−06 
                 −4.19E−07 
                 0.00E+00 
               
               
                 r12* 
                 0 
                 2.59E−04 
                 −9.52E−05 
                 1.55E−05 
                 −1.26E−06 
                 0.00E+00 
               
               
                 r13* 
                 0 
                 6.42E−03 
                 1.61E−04 
                 4.99E−05 
                 6.34E−06 
                 0.00E+00 
               
               
                 r14* 
                 0 
                 1.62E−03 
                 −1.07E−04 
                 1.34E−05 
                 −5.19E−07 
                 0.00E+00 
               
               
                 r15* 
                 0 
                 7.00E−03 
                 −3.18E−05 
                 −5.79E−05 
                 5.71E−06 
                 0.OOE+00 
               
               
                   
               
            
           
         
       
     
      Table 10 indicates, from the left-side column thereof, the respective lens surface numbers, radii of curvature (unit: mm) of the respective lens surfaces, distances (unit: mm) between the respective lens surfaces in the optical axis direction, namely, axial distances between the respective lens surfaces in the infinite focal point at the wide angle limit (W), the mid point (M), and the telephoto limit (T), refractive indices of the respective lens elements, and the Abbe numbers of the respective lens elements. The values in the blank columns regarding the axial distance at the mid point (M) and at the telephoto limit (T) are the same as that in the corresponding left-side column at the wide angle limit (W). The axial distance is a distance calculated on the presumption that the medium residing in the region between a pair of opposing planes including an optical plane and an imaging plane is the air. As shown in  FIG. 22 , the surface denoted by ri (i= 1 ,  2 ,  3 , . . . ) indicates the i-th lens surface from the object side, and the surface ri marked with an asterisk (*) is an aspherical surface, namely, a refractive optical plane of an aspherical configuration or a plane having a refractive power substantially equivalent to the action of an aspherical plane.  
      As is obvious from Table 10, in Example 4, both sides of the lens element (LP 1 ) closest to the object side, both sides of the fifth lens element (L 5 ), and both sides of the lens element (LP 2 ) closest to the imaging side are aspherical. Further, since the aperture stop (ST), both sides of the plane parallel plate (PL), and the light receiving surface of the image sensor (SR) are flat, respective radii of curvature thereof are infinite (∞).  
      The aspherical configuration of the lens element is defined by the following conditional formula (4), wherein the apex of the lens surface is represented as the point of origin, and a local orthogonal coordinate system (x, y, z), with the direction from the object toward the image sensor being the positive z-axis direction is used.  
             z   =         c   ·     h   2         1   +       1   -       (     1   +   k     )     ⁢       c   2     ·     h   2                 +     A   ·     h   4       +     B   ·     h   6       +     C   ·     h   8       +     D   ·     h   10       +     E   ·     h   12                 (   4   )             
 
 where 
      z represents a z-axis displacement at the height position h relative to the apex of the lens surface,     h represents a height in a direction perpendicular to the z-axis (h 2 =x 2 +y 2 ),     c represents a curvature near the apex of the lens surface (=1/radius of curvature),     A, B, C, D, and E respectively represent aspheric coefficients of 4th, 6th, 8th, 10th, and 12th orders, and     k represents a conical coefficient. Table 11 shows the conical coefficient k, and the aspheric coefficients A, B, C, D, and E of the respective lens surfaces. As is obvious from the conditional formula (4), the radii of curvature of the respective aspheric lens elements shown in Table 1 each show a value approximate to the center of the corresponding lens element.    

      The spherical aberration (LONGITUDINAL SPHERICAL ABERRATION in  FIGS. 27A, 27D , and  27 G), the astigmatism (ASTIGMATISM in  FIGS. 27B, 27E , and  27 I), and the distortion aberration (DISTORTION in  FIGS. 27C, 27F , and  27 I) of the optical system having the above lens arrangement and construction in Example 4, namely, the optical system comprised of the first through the fourth lens groups with an infinite focal length are shown in  FIGS. 27A through 27I . Specifically, the respective aberrations at the wide angle limit (W), the mid point (M), and the telephoto limit (T) are shown in the upper row, the intermediate row, and the lower row in  FIGS. 27A through 27I . Each of the horizontal axes in the spherical aberration diagrams and the astigmatism diagrams shows a focal point displacement in the unit of mm. Each of the horizontal axes in the distortion aberration diagrams shows a distortion in terms of percentage. Each of the vertical axes in the spherical aberration diagrams shows a value standardized by the incident height, and each of the vertical axes in the astigmatism diagrams and the distortion aberration diagrams shows a height of an optical image or an image height in the unit of mm.  
      In the spherical aberration diagrams, aberrations in case of using light of three different wavelengths are shown, wherein the one-dotted-chain lines represent aberrations in a red ray (wavelength: 656.27 nm), the solid lines represent aberrations in a yellow ray (so-called “d-ray” having a wavelength of 587.56 nm), and the broken lines represent aberrations in a blue ray (wavelength: 435.83 nm). In the astigmatism diagrams, the dashed lines “S” and “T” respectively represent results on a sagittal (radial) plane and a tangential (meridional) plane. Further, the astigmatism diagrams and the distortion aberration diagrams show results of using the yellow ray or d-ray.  
      As is obvious from  FIGS. 27A through 27I , the lens groups in Example 4 exhibit superior optical characteristics, wherein the spherical aberration, the astigmatism, and the distortion aberration are significantly small at all the positions, namely, at the wide angle limit (W), the mid point (W), and the telephoto limit (T). The focal lengths (unit: mm) and the F-numbers at the wide angle limit (W), the mid point (M), and the telephoto limit (T) in Example 4 are shown in Table 16 and Table 17, respectively. Tables 16 and 17 show that Example 4 provides a fast optical system with a short focal length.  
     Example 5  
      Construction data on the respective lens elements in the zoom optical system  55  as the fifth embodiment (Example 5) are described in Tables 12 and 13. As is obvious from Tables 12 and 13, in Example 5, both sides of the lens element (LP 1 ) closest to the object side, the imaging-side surface of the second lens element (L 2 ), the object-side surface of the third lens element (L 3 ), both sides of the fifth lens element (L 5 ), and both sides of the lens element (LP 2 ) closest to the imaging side are aspherical.  
                               TABLE 10                                  AXIAL DISTANCE               LENS       BETWEEN SUR-               SUR-   RADIUS OF   FACES (INFINITE   REFRAC-   ABBE       FACE   CURVATURE   FOCAL POINT, mm)   TIVE   NUM-                                         No.   (mm)   W   M   T   INDEX   BER               OBJECT   —   ∞   ∞   ∞               r1*   −6.031   7.424           1.58340   30.23       r2*   −5.498   0.741       r3   −4.923   0.574           1.72858   52.48       r4   29.654   0.008           1.51400   42.83       r5   29.654   2.347           1.84666   23.82       r6*   −51.572   6.596   2.807   0.100       r7   ∞   0.574       r8*   5.564   2.000           1.84666   23.82       r9   3.201   0.008           1.51400   42.83       r10   3.201   1.627           1.51389   66.89       r11   −21.826   0.100   1.840   0.791       r12*   4.500   3.200           1.51680   64.20       r13*   5.154   2.587   4.637   8.393       r14*   96.914   6.583           1.51680   64.20       r15*   −6.517   0.000       r16   ∞   0.500           1.51680   64.20       r17   ∞   0.500       r18   ∞                  
 
     
       
         
           
               
               
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                   
               
               
                 LENS SURFACE 
                 CONICAL 
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 No. 
                 COEFFICIENT 
                 A 
                 B 
                 C 
                 D 
                 E 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 r1* 
                 −0.599782 
                 2.00E−03 
                 −1.02E−05 
                 −1.49E−06 
                 7.60E−08 
                 −1.42E−09 
               
               
                 r2* 
                 0 
                 2.27E−03 
                 −5.45E−07 
                 −2.58E−06 
                 2.51E−08 
                 0.00E+00 
               
               
                 r6* 
                 0 
                 −9.01E−04 
                 2.65E−05 
                 −8.48E−07 
                 1.81E−07 
                 0.00E+00 
               
               
                 r8* 
                 0 
                 −7.51E−05 
                 5.04E−05 
                 −1.29E−05 
                 1.38E−06 
                 0.00E+00 
               
               
                 r12* 
                 0 
                 6.51E−04 
                 −8.51E−05 
                 2.54E−05 
                 −1.64E−06 
                 0.00E+00 
               
               
                 r13* 
                 0 
                 4.58E−03 
                 −8.90E−05 
                 8.22E−05 
                 −3.64E−06 
                 0.00E+00 
               
               
                 r14* 
                 0 
                 2.85E−04 
                 1.10E−04 
                 −2.29E−05 
                 1.52E−06 
                 0.00E+00 
               
               
                 r15* 
                 0 
                 9.83E−03 
                 −8.55E−04 
                 4.91E−05 
                 −1.20E−06 
                 0.00E+00 
               
               
                   
               
            
           
         
       
     
     Example 6  
      Construction data on the respective lens elements in the zoom optical system  56  as the sixth embodiment (Example 6) are described in Tables 14 and 15. As is obvious from Tables 14 and 15, in Example 6, the object-side surface of the lens element (LP 1 ) closest to the object side, the imaging-side surface of the second lens element (L 2 ), the object-side surface of the third lens element (L 3 ), the object-side surface of the fifth lens element (L 5 ), and both sides of the lens element (LP 2 ) closest to the imaging side are aspherical.  
                                   TABLE 14                                  AXIAL DISTANCE   AXIAL DISTANCE                       BETWEEN SURFACES   BETWEEN SURFACES       LENS   RADIUS OF   (INFINITE FOCAL   (CLOSEST FOCAL       SURFACE   CURVATURE   POINT, mm)   POINT, mm)   REFRACTIVE   ABBE                                                     No.   (mm)   W   M   T   W   M   T   INDEX   NUMBER                                                             OBJECT   —   ∞   ∞   ∞   200   200   200               r1*   −10.245   8.047                       1.58340   30.23       r2   −3.765   0.030                       1.51400   42.83       r3   −3.765   0.574                       1.82757   54.06       r4   10.431   0.008                       1.51400   42.83       r5   10.431   2.919                       1.84666   23.82       r6*   −595.348   6.161   2.225   0.100   6.532   2.476   0.338       r7   ∞   0.574       r8*   5.109   2.000                       1.84666   23.82       r9   2.989   0.008                       1.51400   42.83       r10   2.989   1.446                       1.54742   63.28       r11   −36.604   2.699   4.307   3.765   2.328   4.056   3.527       r12*   9.589   4.400                       1.51680   64.20       r13   −34.549   0.513   2.841   5.508   0.513   2.841   5.508       r14*   34.039   5.439                       1.51680   64.20       r15*   8.742   1.182       r16   ∞   0.500                       1.51680   64.20       r17   ∞   0.500       r18   ∞                  
 
     
       
         
           
               
               
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                   
               
               
                 LENS SURFACE 
                 CONICAL 
                 ASPHERIC COEFFICIENT 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 No. 
                 COEFFICIENT 
                 A 
                 B 
                 C 
                 D 
                 E 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 r1* 
                 −0.729266 
                 1.10E−03 
                 −1.56E−05 
                 5.33E−07 
                 −1.75E−08 
                 2.93E−10 
               
               
                 r6* 
                 0 
                 1.25E−04 
                 5.99E−05 
                 −1.74E−05 
                 1.08E−06 
                 0.00E+00 
               
               
                 r8* 
                 0 
                 −1.93E−04 
                 4.85E−05 
                 −2.14E−05 
                 3.59E−06 
                 0.00E+00 
               
               
                 r12* 
                 0 
                 −1.14E−04 
                 3.34E−05 
                 −6.98E−07 
                 −9.94E−09 
                 0.00E+00 
               
               
                 r14* 
                 0 
                 −9.69E−04 
                 −3.47E−05 
                 −1.61E−05 
                 9.67E−07 
                 0.00E+00 
               
               
                 r15* 
                 0 
                 3.49E−03 
                 −1.65E−04 
                 −2.82E−05 
                 1.97E−06 
                 0.00E+00 
               
               
                   
               
            
           
         
       
     
      The spherical aberration (LONGITUDINAL SPHERICAL ABERRATION in  FIGS. 28A, 28D ,  28 G,  29 A,  29 D,  29 G,  30 A,  30 D, and  30 G), the astigmatism (ASTIGMATISM in  FIGS. 28B, 28E ,  28 H,  29 B,  29 E,  29 H,  30 B,  30 E, and  30 H), and the distortion aberration (DISTORTION in  FIGS. 28C, 28F ,  28 I,  29 C,  29 F,  291 ,  30 C,  30 F, and  30 I) of the optical systems in Examples 5 and 6 having the above lens arrangement and construction are shown in  FIGS. 28A through 30I . Specifically,  FIGS. 28A through 28I  are aberration diagrams of Example 5 with an infinite focal length,  FIGS. 29A through 29I  are aberration diagrams of Example 6 with an infinite focal length, and  FIGS. 30A through 30I  are aberration diagrams of Example 6 with a closest focal length. As is obvious from  FIGS. 28A through 30I , the lens groups in Examples 5 and 6 exhibit superior optical characteristics, wherein the spherical aberration, the astigmatism, and the distortion aberration are significantly small at all the positions, namely, at the wide angle limit (W), the mid point (W), and the telephoto limit (T).  
      The focal lengths (unit: mm) and the F-numbers at the wide angle limit (W), the mid point (M), and the telephoto limit (T) in Examples 5 and 6 are shown in Table 16 and Table 17, respectively. Tables 16 and 17 show that Examples 5 and 6 provide fast optical systems with a short focal length, as well as Example 4.  
               TABLE 16                          FOCAL LENGTH (mm)                                 W   M   T                                                 EXAMPLE 4   4.9   7.4   9.8           EXAMPLE 5   4.9   7.4   10.8           EXAMPLE 6   4.9   7.4   9.6                      
 
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                   
               
               
                 F NUMBER 
               
            
           
           
               
               
               
               
            
               
                   
                 W 
                 M 
                 T 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 EXAMPLE 4 
                 3.1 
                 3.8 
                 4.5 
               
               
                   
                 EXAMPLE 5 
                 3.3 
                 4.0 
                 5.0 
               
               
                   
                 EXAMPLE 6 
                 3.9 
                 4.6 
                 5.0 
               
               
                   
                   
               
            
           
         
       
     
      The arrangement relations between the second reflecting prism (PR 2 ) and the image sensor (SR) in Examples 4 through 6 are defined as shown in Table 18 to miniaturize the respective zoom optical systems. Specifically, the height a (unit: mm) of the light receiving surface of the image sensor (SR) on the plane where the optical path of the image sensor (SR) is folded, which corresponds to the plane of  FIG. 21  ( FIG. 23  or  FIG. 25 ), the distance d (unit: mm) between the exit surface (S 6 ) of the second reflecting prism (PR 2 ) and the light receiving surface of the image sensor (SR), and the respective calculation results of the conditional formula (1) in Examples 4 through 6 are as shown in Table 18.  
                               TABLE 18                                      HEIGHT (a) OF LIGHT RECEIVING   DISTANCE (d) BETWEEN EXIT               SURFACE OF IMAGE SENSOR   SURFACE OF SECOND REFLECTING           ON PLANE WHERE OPTICAL   PRISM AND LIGHT RECEIVING           PATH IS FOLDED   SURFACE OF IMAGE SENSOR   d/a                                         EXAMPLE 4   3.440   1.484   0.431       EXAMPLE 5   3.440   1.000   0.291       EXAMPLE 6   3.440   2.182   0.634                  
 
      parameters as shown in Table 19 are adopted to optimize the size or the length of the respective second reflecting prisms (PR 2 ) in Examples 4 through 6. Specifically, the refractive index n of each second reflecting prism (PR 2 ), the distance t of the principal ray, the exit pupil distance p, and the respective calculation results of the conditional formula (2) in Examples 4 through 6 are as shown in Table 19, wherein the units of the parameters t and p are mm.  
                               TABLE 19                                   EXAMPLE 4   EXAMPLE 5   EXAMPLE 6                          w (WIDE ANGLE LIMIT)   w (WIDE ANGLE LIMIT)   w (WIDE ANGLE LIMIT)                             REFRACTIVE INDEX (n)   1.517   1.517   1.517       DISTANCE (t) OF PRINCIPAL RAY   6.468   6.583   5.439       EXIT PUPIL DISTANCE (p)   −15.560   −85.726   −10.440       (t · n)/p   −0.631   −0.116   −0.790                                 m (MID POINT)   m (MID POINT)   m (MID POINT)                             REFRACTIVE INDEX (n)   1.517   1.517   1.517       DISTANCE (t) OF PRINCIPAL RAY   6.468   6.583   5.439       EXIT PUPIL DISTANCE (p)   −27.400   81.853   −12.609       (t · n)/p   −0.358   0.122   +0.654                                 t (TELEPHOTO LIMIT)   t (TELEPHOTO LIMIT)   t (TELEPHOTO LIMIT)                             REFRACTIVE INDEX (n)   1.517   1.517   1.517       DISTANCE (t) OF PRINCIPAL RAY   6.468   6.583   5.439       EXIT PUPIL DISTANCE (p)   −57.010   −41.316   −12.772       (t · n)/p   −0.172   −0.242   −0.646                  
 
      Adopting the parameters as shown in Tables 18 and 19 enables to reduce the respective thicknesses of the zoom optical systems  54  through  56  in the fourth through the sixth embodiments in the direction of the arrow L′ in  FIG. 21 , which contributes to miniaturization of the zoom optical systems in the thickness direction thereof.  
      In the first through the sixth embodiments, the first reflecting prism (PR 1 ) is made of a resin or a plastic material, and the optical devices other than the first reflecting prism (PR 1 ) are made of glass. Examples of the invention are not limited to this. It is possible to make a first reflecting prism (PR 1 ) and a second reflecting prism (PR 2 ) of a plastic material, or it is possible to make a part or the entirety of the optical devices including a lens element between the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ) of a plastic material, as well as the first reflecting prism (PR 1 ) and the second reflecting prism (PR 2 ). For instance, using a plastic lens element or plastic lens elements for zooming is advantageous in reducing a load to a lens driver. Such an arrangement contributes to further miniaturization of the entirety of the imaging lens device including a lens group and a lens driver.  
      As described above, since the imaging optical systems  51  through  53  and the zoom optical systems  54  through  56  in the first through the sixth embodiments are compact and lightweight, these optical systems are suitable to be mounted in a digital apparatus, particularly, in a portable apparatus such as the camera phone  200 . Further, since the inventive imaging optical systems and the inventive zoom optical systems have high optical performance compatible with a high-resolution image sensor having two million pixels or more, these optical systems are superior to electronic zoom systems which require interpolation.  
      The invention can take the following modifications in addition to or in place of the foregoing embodiments.  
      (1) In the imaging optical systems and the zoom optical systems of the foregoing embodiments, it is possible to use a cam or a stepping motor in driving the respective lens groups, the aperture stop or the shutter. In the case where a moving amount of the respective lens elements is small or a lens group to be driven is relatively lightweight, it is possible to use a micro-miniature piezoelectric actuator. Such a modification enables to drive the lens groups independently of each other while reducing the size of the driving section or suppressing increase of power consumption, which contributes to further miniaturization of the digital apparatus.  
      (2) In the foregoing embodiments, the subject-side surface of the first reflecting prism and the imaging-side surface of the second reflecting prism are disposed apart from each other at a farthest position in the direction of the arrows A to miniaturize the optical system. Alternatively, it is possible to dispose the subject-side surface of the first reflecting prism and the imaging-side surface of the second reflecting prism at a closest position in the direction of the arrows A, namely, in a region on the same side of the first reflecting prism and the second reflecting prism.  
      Although the present invention has been fully described by way of example with reference to the accompanying drawings, it is to be understood that various changes and modifications will be apparent to those skilled in the art. Therefore, unless otherwise such changes and modifications depart from the scope of the present invention hereinafter defined, they should be construed as being included therein.