Abstract:
A reflective type LCD is provided with a front-light. The front light includes an optical film provided on the large face of a lightguide which faces the liquid crystal display device. A two dimensional area defined by the optical film is greater than a two dimensional area defined by a window formed in the protection member, but less than a two dimensional area defined by the lightguide, so that at least a portion of a peripheral edge of the optical film is located between the end face of the window and the end face of the light guide as viewed from a front of the LCD apparatus.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a reflective type liquid crystal display apparatus that is used for a display function of information display systems, office automation equipment, etc. Specifically, the present invention relates to a reflective type liquid crystal display apparatus including a front light for efficiently illuminating a liquid crystal display device without deteriorating the display quality thereof. Such a display apparatus is therefore preferable for use in portable information terminals or equipment for mobile computing. The present invention also relates to portable electric equipment including such a reflective type liquid crystal display apparatus. 
     2. Description of the Related Art 
     In general, liquid crystal display apparatus can be divided into two groups: a group of transmissive type liquid crystal display apparatus which display letters, images, etc., by adjusting the amount of transmitted light which is emitted from a particular light source; and a group of reflective type liquid crystal display apparatus which display letters, images, etc., using ambient light. 
     The transmissive type liquid crystal display apparatus includes a light source such as a fluorescent light, an electroluminescence (EL) device, or the like, placed on the back surface of a liquid crystal device as a planar light source (backlight). On the other hand, the reflective type liquid crystal display apparatus does not require a backlight because it displays images using ambient light. Thus, the reflective type liquid crystal display apparatus enjoys advantages such as light weight, thin shape, low power consumption, etc. Furthermore, in a highly bright environment in which sunlight is incident directly on the display device, the reflective type liquid crystal display apparatus enables a viewer to observe images more clearly, whereas the transmissive type liquid crystal display apparatus exhibits serious deterioration in the visibility of images. Thus, demands for the reflective type liquid crystal display apparatus have been increasing, and such a reflective type device is more likely for application in portable electronic equipment such as portable information terminals or apparatus for mobile computing. 
     However, it is sometimes impossible for the reflective type liquid crystal display apparatus to provide sufficient display in a dark environment such as nighttime or the like because the reflective type liquid crystal display apparatus uses ambient light for display and the display brightness thereof heavily depends on environmental conditions. Specifically, such a drawback is a major problem in a reflective type liquid crystal display apparatus which uses a color filter for displaying color images or in a reflective type liquid crystal display apparatus which uses polarizing plates. 
     In order to address such a drawback, it has been proposed to provide an illumination device called a front light for illuminating, in the case of insufficient ambient light, a reflective type liquid crystal device from the front face thereof. 
     For example, CX. PAL Vol. 40 (Sony Semiconductor News pp. 26-27) describes an example of such a front light. This document discloses a conventional front light including a light guide for converting a light from a light source into planar emission light, and an optical film composed of a polarizing plate and a quarter-wave plate which are combined and placed on the emission surface side of the light guide. 
     However, the above-described conventional art involves the drawbacks described below. 
     In general, an electronic information apparatus is covered with a case (a protection element) for protecting a liquid crystal display device. The case is provided with a window through which a viewer observes a display screen. For example, referring to FIG. 11A, in a reflective type liquid crystal display apparatus  450 , a window  401   a  is formed in a size larger than a display area  402  which corresponds to a plurality of pixels formed in the reflective type liquid crystal display device. 
     The window  401   a  is designed so that an unobservable display area does not occur (i.e., the entire display area  402  can be seen) even when observed from an oblique direction. This is because peripheral portions  402   y  of the display area  402  cannot be seen when a viewer  400  observes the display area  402  through the window  401   a  from an oblique direction (a direction not vertical to the screen) as shown in FIG.  11 B. The window  401   a  is typically formed larger than the display area  402  by about 1 mm in each direction, in consideration of an attachment margin as well as an unobservable display area  402   y.    
     In a reflective type liquid crystal display apparatus including a front light (an illuminator) for illuminating a reflective type liquid crystal display device, the front light and the liquid crystal display device are covered with a case, and a window is formed in a viewer-side face of the case through which the viewer observes the screen of the liquid crystal display device. 
     In such a structure, when the size of the light guide is too large relative to the size of the window, electronic equipment becomes large, and the portability thereof may therefore deteriorate. Furthermore, in the case where the size of the light guide of the front light is smaller than the size of the window, light leaks from end faces of the light guide when the light is on, which is observable by the viewer. As a result, display quality of the liquid crystal display apparatus significantly deteriorates. 
     Furthermore, in the case where an optical film is provided under a lower surface of the light guide (an opposite side to the viewer), especially when an adhesion layer is provided between the light guide and the optical film, light leaks from the end faces of the light guide, end faces of the optical film, and an interface between the adhesion layer and the light guide. As a result, display quality significantly deteriorates. 
     Yet, CX. PAL Vol. 40 (Sony Semiconductor News pp. 26-27) does not disclose any means of solving such problems. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the present invention, a reflective type liquid crystal display apparatus includes: a reflective type liquid crystal display device for displaying images by reflecting incident light in such a manner that the incident light is separately controlled for each pixel; a front light positioned at a front face side of the reflective type liquid crystal display device, the front light including a light source and a light guide, wherein light emitted from the light source enters the light guide from an end face thereof near the light source, and the light is output from a large face of the light guide which faces the liquid crystal display device; and a protection member for covering the reflective type liquid crystal display device and the front light, wherein a window is formed in the protection member at a front face side of the front light for a viewer to observe the images displayed on the reflective type liquid crystal display device, wherein, at a side of the front light in which the light source is not provided, a distance between an end face of the window formed in the protection member and an end face of light guide adjacent thereto is determined so that light incident in a direction within a desirable viewing angle range passes through a lower face of the light guide. 
     In one embodiment of the present invention, the protection member covers an end portion of the light guide such that distance X 1  between an end face of the window and an end face of the light guide is within the following range:        0   ≦   X1   ≦       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   i            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where t i+1  is a thickness of the (i+1)th layer; n i  and n i+1  are refractive indices of the i-th layer and the (i+1)th layer, respectively; angle θ i  is an angle between a direction of light incident on the i-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; and the relationship n i ×sin θ 1 =n i+1 ×sin θ i+1  is satisfied); and the front light includes g layers; the adjacent layers have different refractive indices; the g-th layer is adjacent to the light guide; and the (g+1)th layer is the light guide. 
     In another embodiment of the present invention, when i=1, n i =1.00. 
     In still another embodiment of the present invention, when i=1, θ 1 =80°. 
     In still another embodiment of the present invention, the protection member covers an end portion of the light guide such that distance X 1  between an end face of the window and an end face of the light guide is within the following range:            ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       ≦   X1   ≦       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where t i+1  is a thickness of the (i+1)th layer: n i  and n i+1  are refractive indices of the i-th layer and the (i+1)th layer, respectively; angle θ i  is an angle between a direction of light incident on the i-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; angle φ i  is an angle between a direction of light incident on the i-th layer and a direction perpendicular to the front light; the angle φ 1  in the 1st layer is a perspective angle; and the relationships n i ×sin θ i =n i+1 ×sin θ i+1 , and n i ×sin φ i =n i+1 ×sin φ i+1  are satisfied); and the front light includes g layers; the adjacent layers have different refractive indices; the g-th layer is adjacent to the light guide; and the (g+1)th layer is the light guide. 
     In still another embodiment of the present invention, the perspective angle φ 1 , in the 1st layer (i=1) is smaller than 4°. 
     In still another embodiment of the present invention, the front light further includes an optical film positioned on a large face of the light guide which faces the reflective type liquid crystal display device. 
     In still another embodiment of the present invention, at a side in which the light source is not provided, the protection member covers an end portion of the optical film such that distance X 3  between an end face of the window and an end face of the optical film is within the following range:        0   ≦   X3   ≦       ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where t k+1  is a thickness of the (k+1)th layer; n k  and n k+1  are refractive indices of the k-th layer and the (k+1)th layer, respectively: angle θ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light: the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; and the relationship n k ×sin θ k =n k+1 ×sin θ k+1  is satisfied): and the front light includes m layers; the adjacent layers have different refractive indices; the m-th layer is the light guide; and the (m+1)th layer is the optical film. 
     In still another embodiment of the present invention, when k=1, n i =1.00. 
     In still another embodiment of the present invention, when k=1, θ 1 =80°. 
     In still another embodiment of the present invention, the protection member covers an end portion of the optical film such that distance X 3  between an end face of the window and an end face of the optical film is is within the following range:            ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       ≦   X3   ≦       ∑     k   =   1     m          (       t     k   +   1       /     tan        (     90   -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where t k+1  is a thickness of the (k+1)th layer: n k  and n k+1  are refractive indices of the k-th layer and the (k+1)th layer, respectively; angle θ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; angle φ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light; the angle φ 1  in the 1st layer is a perspective angle; and the relationships n k ×sin θ k =n k+1 ×sin θ k+1 , and n k ×sin φ k =n k+1 ×sin φ k+1  are satisfied); and the front light includes m layers; the adjacent layers have different refractive indices; the m-th layer is the light guide; and the (m+1)th layer is the optical film. 
     In still another embodiment of the present invention, the perspective angle φ 1  in the 1st layer (k=1) is smaller than 4°. 
     In still another embodiment of the present invention, the optical film has an anti-reflection effect. 
     In still another embodiment of the present invention, the optical film includes a polarizing plate and a quarter-wave plate. 
     In still another embodiment of the present invention, the optical film includes a polarizing plate, a half-wave plate, and a quarter-wave plate. 
     According to another aspect of the present invention, portable electronic equipment includes the reflective type liquid crystal display apparatus of claim 1. 
     According to still another aspect of the present invention, a reflective type liquid crystal display apparatus includes: a reflective type liquid crystal display device for displaying images by reflecting incident light in such a manner that the incident light is separately controlled for each pixel; a front light positioned at a front face side of the reflective type liquid crystal display device, the front light including a light source and a light guide, wherein light emitted from the light source enters the light guide from an end face thereof near the light source, and the light is output from a large face of the light guide which faces the liquid crystal display device; and a protection member for covering the reflective type liquid crystal display device and the front light, wherein a window is formed in the protection member at a front face side of the front light for a viewer to observe the images displayed on the reflective type liquid crystal display device, wherein, at a side of the front light in which the light source is provided, a distance between an end face of the window formed in the protection member and an end face of light guide adjacent thereto is determined so that light which is emitted from the light source and reflected by a lower face of the front light is not observed by the viewer. 
     In one embodiment of the present invention, the protection member covers an end portion of the light guide such that distance X 2  between an end face of the window and an end face of the light guide is within the following range:        0   ≦   X2   ≦       {       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     (where t i+1  is a thickness of the (i+1)th layer; n i  and n i+1  are refractive indices of the i-th layer and the (i+1)th layer, respectively, angle θ i  is an angle between a direction of light incident on the i-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; and the relationship n i ×sin θ i =n i+1 ×sin θ i+1  is satisfied); and the front light includes g layers; the adjacent layers have different refractive indices: the g-th layer is adjacent to the light guide; and the (g+1)th layer is the light guide. 
     In another embodiment of the present invention, when i=1, n 1 =1.00. 
     In still another embodiment of the present invention, when i=1, θ 1 =80°. 
     In still another embodiment of the present invention, the protection member covers an end portion of the light guide such that distance X 2  between an end face of the window and an end face of the light guide is within the following range:              ∑     j   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   ϕ   g       )         )         )       ≦   X2   ≦       {       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     (where t i+1  is a thickness of the (i+1)th layer; n i  and n i+1  are refractive indices of the i-th layer and the (i+1)th layer, respectively; angle θ i  is an angle between a direction of light incident on the L-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; angle φ i  is an angle between a direction of light incident on the i-th layer and a direction perpendicular to the front light: the angle φ 1  in the 1st layer is a perspective angle: and the relationships n i ×sin θ i =n i+1 ×sin θ i+1 , and n i ×sin φ i =n i+1 ×sin φ i+1  are satisfied); and the front light includes g layers; the adjacent layers have different refractive indices; the g-th layer is adjacent to the light guide; and the (g+1)th layer is the light guide. 
     In still another embodiment of the present invention, the perspective angle φ 1  in the 1st layer (i=1) is smaller than 4°. 
     In still another embodiment of the present invention, the front light further includes an optical film positioned on a large face of the light guide which faces the reflective type liquid crystal display device. 
     In still another embodiment of the present invention, at a side in which the light source is provided, the protection member covers an end portion of the optical film such that distance X 4  between an end face of the window and an end face of the optical film is within the following range:        0   ≦   X4   ≦       {       ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where t k+1  is a thickness of the (k+1)th layer; n k  and n k+1  are refractive indices of the k-th layer and the (k+1)th layer, respectively; angle θ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light: the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; and the relationship n k ×sin θ k =n k+1 ×sin θ k+1  is satisfied); and the front light includes m layers; the adjacent layers have different refractive indices; the m-th layer is the light guide: and the (m+1)th layer is the optical film. 
     In still another embodiment of the present invention, when k=1, n 1 =1.00. 
     In still another embodiment of the present invention, when k=1, θ 1 =80°. 
     In still another embodiment of the present invention, the protection member covers an end portion of the optical film such that distance X 4  between an end face of the window and an end face of the optical film is within the following range:              ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   ϕ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   ϕ   m       )         )         )       ≦   X4   ≦       {       ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where t k+1  is a thickness of the (k+1)th layer: n k  and n k+1  are refractive indices of the k-th layer and the (k+1)th layer, respectively: angle θ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light; the angle θ 1  in the 1st layer is a maximum angle within a desirable viewing angle range; angle φ k  is an angle between a direction of light incident on the k-th layer and a direction perpendicular to the front light; the angle φ 1  in the 1st layer is a perspective angle; and the relationships n k ×sin θ k =n k+1 ×sin θ k+1 , and n k ×sin φ k =n k+1 ×sin φ k+1  are satisfied); and the front light includes m layers; the adjacent layers have different refractive indices; the m- th layer is the light guide; and the (m+1)th layer is the optical film. 
     In still another embodiment of the present invention, the perspective angle in the 1st layer (k=1) is smaller than 4°. 
     In still another embodiment of the present invention, the optical film has an anti-reflection effect. 
     In still another embodiment of the present invention, the optical film includes a polarizing plate and a quarter-wave plate. 
     In still another embodiment of the present invention, the optical film includes a polarizing plate, a half-wave plate, and a quarter-wave plate. 
     According to still another aspect of the present invention, portable electronic equipment includes the reflective type liquid crystal display apparatus of claim 17. 
     Hereinafter, the functions of the present invention will be described. 
     As described above, window  401   a  is provided in a viewer&#39;s side face of a protection member (case) that protects a liquid crystal display device such that an entire display area can be seen even from an oblique direction. However, when the area of the front face of the light guide is smaller than the area of the window  401   a , light leaks from peripheral end faces of the light guide, resulting in significant deterioration of the display quality. In order to address such a drawback, a distance X 1  (FIG. 1B) between an end face of the light guide and an end face of the window corresponding thereto is set in a range of 0≦X 1 , so that the peripheral portion of the light guide is covered with a case. In the case where the display area of the liquid crystal display device is small, the distance X 1  may also be small. In this case, the end face of the window and the end face of the light guide are observed substantially in the same viewing direction. When the end face of the light guide is located outside the end face of the window, i.e., 0≦X 1 , light leakage from the end faces of the light guide does not occur. 
     A typical liquid crystal display device has a viewing angle range up to about 80° from a direction perpendicular to a screen of the liquid crystal display device (angle 0°). Thus, the light guide may be designed in a size such that the viewing angle range up to about 80° is considered, and thus it is not necessary to design the light guide larger than such a size. 
     The “viewing angle range” of the liquid crystal display device used herein represents a range in which displayed images can be normally seen, excluding a case where a viewer cannot correctly recognize displayed images. Outside the viewing angle range, a black displayed image may appear whitish, or gray-scale inversion may occur, resulting in the deterioration in the contrast or the inversion of the contrast. 
     As described above, a large-size light guide results in a large-size electronic equipment, whereby portability of the electronic equipment may be reduced. In the present invention, for the purpose of avoiding such a drawback, at a side of a light guide in which a light source is not provided, an end portion of the light guide is covered with a case so that the distance X 1  between the end face of the light guide and the end face of the window is within the following range:        0   ≦   X1   ≦       ∑     j   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in an air layer of the window (i=1), n 1 =1.00 and θ 1 =80°). With such an arrangement, light leakage from the end faces of the light guide and the unnecessary reflected light can be prevented over the viewing angle range from 0° (lower limit) to 80° (upper limit) without spoiling the portability of the liquid crystal display apparatus. Thus, such a liquid crystal display apparatus can be applied to a large-size screen which requires a large viewing angle range, as well as a small-size screen which does not require a large viewing angle range. Furthermore, such a liquid crystal display apparatus is suitable for use in a small-size electronic information apparatus of low power consumption. 
     An observable area for the viewer should be considered in order to prevent light leakage from the light guide. For example, as shown in FIG. 8, in the case where the viewer observes the center of a 2″ reflective type liquid crystal display device (panel  800 ) in a direction substantially perpendicular to the panel  800  from a position which is 300 mm away from the panel  800 , an area corresponding to an angle of 3.87° (about 4°) in the horizontal direction and an angle of 2.91° (about 3°) in the vertical direction can be observed. 
     Therefore, in the case where the light guide is provided in front of the liquid crystal display device, the light guide is positioned so as to cover the entire area corresponding to a perspective angle, whereby light leakage from the end face of the light guide can be prevented from reaching the viewer&#39;s eye. For example, in the case of employing a 2″ reflective type liquid crystal display device, the light guide is designed and positioned so as to cover the entire area corresponding to a perspective angle of about 3°, whereby light leakage toward the viewer can be prevented. More preferably, an area corresponding to a perspective angle of about 4° is considered. In the case of employing a 2″ or greater reflective type liquid crystal display device, the perspective angle becomes larger, and an area corresponding there to also becomes larger. In such a case, it is preferable that the light guide is designed and positioned, in consideration of a viewing angle characteristic of the liquid crystal display device, so as to cover an area corresponding to a viewing angle range up to about 80° or smaller. Thus, in the present invention, at the side in which the light source is not provided, it is preferable that the end portion of the light guide is covered with the case so that distance X 1  between the end face of the window and the end face of the light guide is within the following range:            ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       ≦   X1   ≦       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in the air layer of the window (i=1), perspective angle φ 1  is smaller than 4°). With such an arrangement, even in the case of employing a front light for illuminating a small-size liquid crystal display device, light leakage is prevented, and the display quality therefore improves. 
     Furthermore, according to a viewing angle range required by the liquid crystal display device, at the side in which the light source is not provided, it is preferable that the case covers the end portion of the light guide so that distance X 1  between the end face of the window and the end face of the light guide is within the following range:            ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       ≦   X1   ≦       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in the air layer of the window (i=1), φ 1  is a required perspective angle). With such an arrangement, light leakage can be prevented in accordance with a viewing angle characteristic of the liquid crystal display device, and the display quality therefore improves. 
     On the other hand, at a side in which the light source is provided, relative to the sides in which the light source is not provided, the intensity of light from the light source is greater, and the light emitted from the light source and reflected by the lower face of the light guide should be prevented from reaching the viewer&#39;s eye. 
     For example, assume an exemplary arrangement in which a touch panel  908 , which serves as an input/output device, is provided at the viewer side of the light guide  907  as shown in FIG.  9 A. At a side in which the light source  909  is provided (light source side), light incident in the direction of maximum viewing angle θ 1  (light introduced from an air layer  901  (i=1)) travels through a PET film  902 , a transparent electrode  903 , an air layer  904 , a transparent electrode  905 , a glass substrate  906 , and a light guide  907 , and reaches the lower face of the light guide  907  (route R 1 ). The traveling light is refracted by respective interfaces between adjacent layers according to Snell&#39;s law. Thus, while traveling from the upper face of the PET film  902  to the lower face of the light guide  907  which is provided as the (g+1)th layer (7th layer in this example), the light shifts by distance X 1  in the horizontal direction. (It should be noted that the front light herein includes g layers.) As shown in FIG. 6A, at a side in which the light source is not provided, the distance between the end face of the window and the end face of the light guide  607  is only required to be larger than X 1 . For reference, distance X 1  is shown in FIG.  9 A. As shown in FIG. 9A, at a side in which the light source  909  is provided, in order to prevent light which is emitted from the light source  909  and then reflected by the lower face of the light guide  907  from traveling through route R 1  to reach the viewer&#39;s eye, distance X 2  between the end face of the case  900  and the end face of the light guide  907  needs to include distance α in addition to distance X 1 . Since a portion of the light emitted from the light source  909  is reflected by the lower face of the light guide  907  as shown in FIG. 9B (a partially enlarged view of FIG.  9 A), distance a is determined in consideration of angle θ 7 , the thickness t 7  of the light guide  907 , and the refractive index of the light guide  907 . Thus, in the present invention, at the light source side, it is preferable that an end portion of the light guide is covered with the case so that distance X 2  between the end face of the window and the end face of the light guide is within the following range:        0   ≦   X2   ≦       {       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                   sin   i       )         )         )       }     +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     With such an arrangement, in a viewing angle range from 0° (lower limit) to preferably 80° (upper limit), light leakage from the end face of the light guide is prevented, and the light emitted from the light source and then reflected by the lower face of the light guide is prevented from reaching the viewer s eye, without spoiling the portability of the liquid crystal display apparatus. 
     Furthermore, also at the light source side, it is preferable that distance X 2  between the end face of the window of the case and the end face of the light guide is set in consideration of a length corresponding to prospective angles of the panel as described above (e.g., in a 2″ reflective type liquid crystal display device, about 3° in the vertical direction, and about 4° in the horizontal direction). 
     For example, it is preferable that the case covers the end portion of the light guide so that distance X 2  between the end face of the window and the end face of the light guide is within the following range:              ∑     j   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   ϕ   g       )         )         )       ≦   X2   ≦       {       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     (where, in the air layer of the window (i=1), φ 1  is a required perspective angle). With such an arrangement, light leakage can be prevented in accordance with a viewing angle characteristic of the liquid crystal display device, and the display quality therefore improves. 
     Alternatively, in the case where an optical film is provided on a lower face of the light guide, light leaks from peripheral end faces of the optical film. Thus, it is preferable that the end faces of the optical film is covered with the case so that, at the side in which the light source is not provided as shown in FIG. 7, distance X 3  between the end face of the window and the end face of the optical film is within the following range:        0   ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the air layer of the window (k=1), n 1 =1.00, θ 1  is within a desirable viewing angle range (preferably 80°)). 
     In such a case, at the side in which the light source is not provided, considering an area corresponding to a particular perspective angle (with respect to the end face of the window), it is also preferable that the end portion of the optical film is covered with the case so that distance X 3  between the end face of the window and the end face of the optical film is within the following range:            ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a desirable perspective angle). 
     Furthermore, it is preferable that, at the side in which the light source is not provided, the end portion of the optical film is covered with the case so that distance X 3  between the end face of the window and the end face of the optical film is set, in accordance with a viewing angle range required for the liquid crystal display device, to be within the following range:            ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a required perspective angle). 
     Furthermore, also in the case where an optical film is provided on the lower face of the light guide, at the light source side, relative to the side in which the light source is not provided, the intensity of light from the light source is greater, and the light emitted from the light source and then reflected by the lower face of the light guide should be prevented from reaching the viewer&#39;s eye. 
     For example, assume an exemplary arrangement in which a touch panel  1010 , which serves as an input/output device, is provided at the viewer side of the light guide  1007  as shown in FIG.  10 A. At a side in which the light source  1011  is provided (light source side), light incident in the direction of maximum viewing angle θ 1  (light introduced from an air layer  1001  (k=1)) travels through a PET film  1002 , a transparent electrode  1003 , an air layer  1004 , a transparent electrode  1005 , a glass substrate  1006 , a light guide  1007 , and an optical film  1008 , and reaches the lower face of the optical film  1008  (route R 2 ). The traveling light is refracted by respective interfaces between adjacent layers according to Snell&#39;s law. Thus, while traveling from the upper face of the PET film  1002  to the lower face of the light guide  1007  which is provided as the (m+1)th layer (8th layer in this example), the light shifts by distance X 3  in the horizontal direction. (It should be noted that the front light herein includes layers.) As shown in FIG. 7, at a side in which a light source is not provided, a distance between an end face of the case and an end face of the optical film  708  is only required to be larger than X 3 . As shown in FIG. 10A, at a side in which a light source  1011  is provided, in order to prevent light which is emitted from the light source  1011  and reflected by the lower surface of the optical film  1008  from traveling through route R 2  to reach the viewer&#39;s eye, distance X 4  between the end face of the window formed in the case  1000  and the end face of the optical film  1008  needs to include distance β in addition to distance X 3 . Since a portion of the light emitted from the light source  1011  is reflected by the lower face of the optical film  1008  as shown in FIG. 10B (a partially enlarged view of FIG.  10 A), distance β is determined in consideration of angle θ 7 , angle θ 8 , the thicknesses t 6  and t 7  of the light guide  1007  and the optical film  1008 , and the refractive indices of the light guide  1007  and the optical film  1008 . Thus, in the present invention, at the light source side, it is preferable that an end portion of the optical film is covered with the case so that distance X 4  between the end face of the window and the end face of the optical film is within the following range:        0   ≦   X4   ≦       {       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a required perspective angle). With such an arrangement, in a viewing angle range from 0° (lower limit) to preferably 80° (upper limit), light reflection which occurs in a direction of the thickness of the optical film, and light reflection by the optical film which occurs around the optical film due to insufficient compensation of a phase by the optical film, can be prevented. 
     Furthermore, also at the light source side, it is preferable that distance X 3  between the end face of the window of the case and the end face of the optical film is set in consideration of a length corresponding to prospective angles of the panel as described above (e.g., in a 2″ reflective type liquid crystal display device, about 3° in the vertical direction, and about 4° in the horizontal direction). 
     For example, it is preferable that, at the side in which the light source is provided, the end portion of the optical film is covered with the case so that distance X 4  between the end face of the window and the end face of the optical film is set, in accordance with a viewing angle range required for the liquid crystal display device, to be within the following range:              ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   ϕ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   ϕ   m       )         )         )       ≦   X4   ≤       {       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a required perspective angle). 
     In the case where a film having an anti-reflection effect is employed as the optical film, interference between light emitted from the light source and light reflected by an emission surface of the light guide (a large face of the light guide which faces the liquid crystal display device) can be prevented. 
     In the case where a film composed of a polarizing plate and a quarter-wave plate is employed as the optical film, unnecessary reflection light reflected by the quarter-wave plate or by a surface of a counter (upper) glass substrate of the liquid crystal display device is removed, whereby contrast deterioration can be prevented. 
     Alternatively, in the case where a film composed of a polarizing plate, a half-wave plate, and a quarter-wave plate is employed as the optical film, the tolerance of the phase delay with respect to the wavelength of the light is compensated for, whereby a circularly polarized state of light can be maintained. As a result, unnecessary reflection light reflected by the quarter-wave plate or by a surface of a counter glass substrate of the liquid crystal display device can be further prevented. 
     In the specification of the present invention, light incident in the direction of maximum viewing angle is considered. The route of the incident light (for example, route R 1  of FIGS. 9 or route R 2  of FIG. 10) is identical to a route of light leaking from the reflection surface to the viewer&#39;s eye, although a direction of travelling light is inversive. Thus, it is apparent to those skilled in the art that the distance between the end face of the light guide and the end face of the window of the case or the distance between the end face of the optical film and the end face of the window of the case can be determined based on the route of the incident light so that the light lea)age through the same route can be prevented. 
     Thus, the invention described herein makes possible the advantage of providing a reflective type liquid crystal display apparatus and a portable electric device in which light leakage from (nd faces of a light guide or an optical film is prevented, without spoiling the portability of the apparatus and the: equipment, thereby increasing display quality. 
     This and other advantages; of the present invention will become apparent to those skilled in the art upon reading and understanding the. following detailed description with reference to the accompanying figures. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a cross-sectional view showing a schematic structure of a reflective type liquid crystal display apparatus according to an embodiment of the present invention. FIG. 1B is a plan view of the reflective type liquid crystal display apparatus shown in FIG.  1 A. 
     FIG. 2A is a perspective view showing a schematic structure of a front light of the reflective type liquid crystal display apparatus; shown in FIGS. 1A and 1B. FIG. 2B is an enlarged view showing a periodic structure formed in the upper face of the light guide. 
     FIG. 3 is a cross-sectional view showing a schematic structure of a reflective type liquid crystal display device shown in FIG.  1 A. 
     FIG. 4A is a cross-sectional view showing a structure of the liquid crystal display apparatus at a side thereof in which the light source is not provided, and illustrating geographical relationships between the case and the light guide, and between the case and the optical film. 
     FIG. 4B is a cross-sectional view showing a structure of the liquid crystal display apparatus at a side thereof in which the light source is provided, and illustrating geographical relationships between the cover and the light guide, and between the cover and the optical film. 
     FIG. 4C is a cross-sectional view showing a structure of the liquid crystal display apparatus at a side thereof in which the light source is not provided, and illustrating a geographical relationship between the cover and the light guide. 
     FIG. 4D is a cross-sectional view showing a structure of the liquid crystal display apparatus at a side thereof in which the light source is provided, and illustrating a geographical relationship between the cover and the light guide. 
     FIG. 5 is a perspective view showing a change in the state of light which transmits through the optical film composed of a polarizing plate and a quarter-wave plate. 
     FIG. 6 shows an exemplary arrangement of the liquid crystal display apparatus in which a touch panel is provided at the viewer&#39;s side of the light guide. Herein, a relationship between an end face of the light guide and the end face of the window formed in the case, at a side in which the light source is not provided, is schematically shown. 
     FIG. 7 shows an exemplary arrangement of the liquid crystal display apparatus in which a touch panel is provided at the viewer is side of the light guide, and an optical film is provided on the lower face of the light guide. Herein, a relationship between the end face of the window formed in the case and an end face of the optical film, at a side of the display apparatus in which the light a source is not provided, is schematically shown. 
     FIG. 8 is a perspective view illustrating a perspective angle for a 2″ reflective type liquid crystal display device when a viewer observes a panel of the display device. 
     FIG. 9A shows an exemplary arrangement of the liquid crystal display apparatus in which a touch panel is provided at a viewer&#39;s side of the light guide. Herein, a relationship between an end face of the light guide and an end face of a window formed in a case, at a side in which a light source is provided, is shown. FIG. 9B is a partially enlarged view of FIG.  9 A. 
     FIG. 10A shows an exemplary arrangement of the liquid crystal display apparatus in which a touch panel is provided at a viewer&#39;s side of the light guide. Herein, a relationship between an end face of the optical film and an end face of a window formed in a case, at a side in which a light source is provided, is shown. FIG. 10B is a partially enlarged view of FIG.  10 A. 
     FIG. 11A is a plan view showing a conventional reflective type liquid crystal display apparatus. FIG. 11B is a cross-sectional view of the reflective type liquid crystal display apparatus shown in FIG.  11 B. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, an embodiment of the present invention will be described with reference to the attached drawings. 
     FIG. 1A is a cross-sectional view showing a structure of a reflective type liquid crystal display apparatus  100  according to the present embodiment. FIG. 1B is a plan view of the reflective type liquid crystal display apparatus  100  shown in FIG.  1 A. 
     The reflective type liquid crystal display apparatus  100  includes a front light  110  at a front face side (viewer&#39;s side) of the reflective type liquid crystal display device  106 . 
     The front light  110  includes a light source  101 , a diffuse reflection sheet  103  covering the light source  101 , a light guide  102 , and an optical film  105  provided at a back face side of the light guide  102 . Light from the light source  101  enters the light guide  102  through an end face  102   a  thereof, and exits from a wide face (emission surface)  102   b  toward a reflective type liquid crystal display device  106 . The light source  101 , the diffuse reflection sheet  103 , the front light  110 , and the reflective type liquid crystal display device  106  are contained in a case (protection member)  104 . The case  104  is provided with a window  104   a  formed in a front face thereof, as shown in FIG.  1 A. 
     As shown in FIG. 1B, the window  104   a  is formed so as to include a display area  116 . The light guide  102  is formed so as to be larger than the window  104   a . The optical film  105  is also formed so as to be larger than the window  104   a.    
     FIG. 2A is a perspective view showing a schematic structure of the front light  110  of the reflective type liquid crystal display apparatus  100  shown in FIGS. 1A and 1B. FIG. 2B is an enlarged view showing a periodic structure  102   f  of the light guide  102 . As shown in FIG. 2A, the optical film  105  includes a polarizing plate  105   a , a half-wave plate  105   b , and a quarter-wave plate  105   c  from the viewer&#39;s side. The total thickness of the optical film  105  is 0.45 mm, and the refractive index thereof is about 1.50. 
     In the present embodiment, the light guide  102  is formed of polymethylmethacrylate (refractive index: n=1.49) by injection molding into a parallel plate having a thickness of 1 mm. An upper face  102   g  of the light guide  102  opposite to the emission surface  102   b  is formed so as to have a periodic structure 102f consisting of a plurality of prisms, in which each prism has a propagation portion  102   d  and a reflection portion  102   e . Referring to FIG. 2B, the periodic structure  102   f  is formed such that a pitch P of the periodic structure  102   f  is 0.39 mm, a width P 1  of the propagation portion  102   d  is 0.38 mm, a width P 2  of the reflection portion  102   e  is 0.1 mm, and the inclination angle of the reflection portion  102   e  is about 45°. With such a structure, the light guide  102  can convert light from the light source  101  into a planar light output from the emission surface  102   b , so as to illuminate the reflective type liquid crystal display device  106 . 
     FIG. 3 is a cross-sectional view showing a schematic structure of the reflective type liquid crystal display device  106  of the reflective type liquid crystal display apparatus  100 . The reflective type liquid crystal display device  106  includes a counter (upper) substrate  120 , a TFT (thin film transistor) substrate (lower substrate)  121 , and a liquid crystal layer  109  interposed between these substrates. The counter substrate  120  includes a glass substrate  106   a , and a color filter  107  and a transparent electrode  108  formed thereon. The TFT substrate  121  includes a glass substrate  106   b , and a plurality of TFT elements (not shown) and a reflection electrode  108   b  formed thereon. 
     As shown in FIGS. 1A and 1B, in the reflective type liquid crystal display apparatus  100 , the case  104  is provided so as to cover a periphery of the reflective type liquid crystal display device  106  and the front light  110 . At the front face side of the front light  110 , the case  104  is provided with the window  104   a , through which a viewer observes displayed images. In FIG. 1B, distance X 1  is a distance, at a side in which the light source  101  is not provided, between an end face  104   a - 1  of the window  104   a  and an end face of the light guide  102 . In the specification of the present application, “a side in which a light guide is not provided” may refer to any of sides other than the side in which a light source is provided (e.g., in FIG. 1B, any of the upper, lower, and right sides). Distance X 2  is a distance, at the side in which the light source  101  is provided, between an end face  104   a - 2  of the window  104   a  and an end face of the light guide  102 . Distance X 3  is a distance, at the side in which the light source  101  is not provided, between an end face  104   a - 1  of the window  104   a  and an end face of the optical film  105 . Distance X 4  is a distance, at the side in which the light source  101  is provided, between an end face  104   a - 2  of the window  104   a  and an end face of the optical film  105 . 
     In the present embodiment, the reflective type liquid crystal display device  106  is a 3.9″ reflective type liquid crystal display device wherein the display area  116  is 59.4 mm×79.2 mm (vertical×horizontal). Furthermore, the size of the window  104   a  of the case  104  is 61.4 mm×81.2 mm (vertical×horizontal), which is larger than that of the display area  116  by 1 mm in all directions, so that the entire display area can be observed. Furthermore, in order to prevent light leakage from end faces of the light guide, the size of the light guide  102  is set to 64.7 mm×83.8 mm (vertical×horizontal), and the size of the optical film  105  is set to 63.7 mm×82.8 mm (vertical×horizontal). 
     Hereinafter, the mechanism of the reflective type liquid crystal display apparatus  100  for preventing light leakage will be described. 
     FIG. 4A shows a structure of the liquid crystal display apparatus  100  at the side in which the light source  201  is not provided, and illustrates a geographical relationship between the end face  102   c  of the light guide  102  and the end face  105   a  of the optical film  105 . FIG. 4B shows a structure of the liquid crystal display apparatus  100  at the light source side, and illustrates geographical relationships between the case  104  and the light guide  102 , and between the case  104  and the optical film  105 . 
     Referring to FIG. 4A, in the case where a viewer  111  observes a peripheral portion of the display area  116  from the direction of an angle θ 1 (=40°), considering the refractive index nd of the light guide  102  (nd=1.49) and the thickness td of the light guide  102  (td=1.00 mm), θ 2  can be determined by the following expression: 
     
       
         1.00 (refractive index of air)×sin θ 1 =nd×sin θ 2   
       
     
     Thus, the viewer  111  observes a position on the upper face of the optical film  105 , which is horizontally an additional distance X from an observed position on the upper surface of the light guide  102  as calculated as follows: 
       X=td /(tan(90°−θ 2 )) 
     
       
         = td /(tan(90°−sin −1 (sin40 °/nd ))) 
       
     
     
       
         =0.48 mm. 
       
     
     That is, the viewer  111  observes a position on the upper face of the optical film  105 , which is horizontally an additional distance of 0.48 mm from the observed position on the upper surface of the light guide  102 . 
     Furthermore, considering the refractive index nk (=1.50) of the optical film  105  and the thickness tk (=0.45 mm) of the optical film  105 , θ 3  is determined by the following expression: 
     
       
           nd ×sin θ 2   =nk ×sin θ 3   
       
     
     Thus, the viewer  111  observes a position on the upper face of the optical film  105 , which is horizontally an additional distance X′ from the observed position on the upper surface of the light guide  102  as calculated as follows: 
     
       
           X′=X+tk /(tan(90°−θ 3 )) 
       
     
     
       
         =0.70 mm 
       
     
     Alternatively, referring to FIG. 4C, in the case where a front light having no optical film is employed, if distance X 1  between the end face  104   a - 1  of the window  104   a  and the end face  102   c  of the light guide  102  is smaller than 0.48 mm, unnecessary reflected light reaches the viewer&#39;s eye without being interrupted by the case  104 , whereby the display quality deteriorates. That is, at the side of the light guide in which the light source is not provided, a distance X 1  between the end face  104   a - 5  of the case  104  and the end face  102   c  is determined so that any light incident in a direction within a desirable viewing angle range passes through the lower face of the light guide  102 , whereby undesirable reflection light can be prevented. 
     Referring to FIG. 4D, also in the case where a front light having no optical film is employed, at a side in which a light source is not provided, if distance X 2  between the end face  104   a - 2  of the window  104   a  and the end face  10   a  of the light guide  102 , is larger than 2X (herein, 0.96 mm), unnecessary light is prevented from reaching the viewer&#39;s eye. 
     In the present embodiment, referring to FIGS. 4A and 4C, distance X 1  between the end face  104   a - 1  of the window  104   a  and the end face  102   c  of the light guide  102  is set to be equal to or more than distance X (e.g., set to 1.3 mm), and distance X 3  between the end face  104   a - 1  of the window  104   a  and the end face  105   a  of the optical film  105  is set to a value equal to or more than distance X′ (e.g., set to 0.8 mm). With such an arrangement, unnecessary light reflected by the light guide  102  or the optical film  105  can be prevented from reaching the viewer&#39;s eye, whereby the display quality is improved. 
     On the other hand, at the side in which the light source  101  is provided as shown in FIG. 4B, under the same condition as those set in FIG. 4A, the intensity of light emitted from the light source  101  is greater than that at the side in which the light source  101  is not provided. Therefore, it is preferable that an end face  102   a  of the light guide  102  is set such that distance X 4  between an end face  104   a - 2  of the window  104  and an end face  105   b  of the optical film  105  is greater than a distance in which unnecessary light reflected by the light guide  102  and the optical film  105  can be prevented from reaching the viewer&#39;s eye (i.e., distance X′ plus distance β (FIG.  10 B)). 
     Considering the reflection of light by the optical film  105 , since 
     
       
           nd ×sin θ 2   =nk ×sin θ 3 , 
       
     
     the viewer  111  observes a position on the upper face of the light guide  102 , which is horizontally an additional distance X″ from an observed position on the upper surface of the light guide  102  as calculated as follows: 
     
       
           X″=X′+tk /(tan(90°−θ 3 )) 
       
     
     
       
         =0.92 mm. 
       
     
     According to the present invention, distance X 4  between the end face  104   a - 2  of the window  104   a  and the end face  105   b  of the optical film  105  is set to a value greater than 0.92 mm (e.g., 1.50 mm), whereby unnecessary reflected light can be prevented from reaching the viewer&#39;s eye, and the display quality is improved, accordingly. 
     Furthermore, considering unnecessary light reflected by the optical film  105  and transmitted through the light guide  102 , since 
     
       
           nd ×sin θ 2   =nk ×sin θ 3 , 
       
     
     the viewer  111  observes a position on the upper face of the light guide  102 , which is horizontally an additional distance X′″ from the observed position on the upper face of the light guide  102  as calculated as follows: 
     
       
         
           X′″=X″+x 
         
       
     
     
       
         =1.40 mm. 
       
     
     Thus, according to the present embodiment, distance X 2  between the end faces 104 a - 2  of the window  104   a  and the end face  102   a  of the light guide  102  is set to be greater than 1.40 mm. In such an arrangement, unnecessary reflected light, which is not interrupted by the case  104 , is prevented from reaching the viewer&#39;s eye, whereby the display quality can be improved. That is, at the side of the front light  110  in which the light source  101  is provided, distance X 2  between the end face  104   a - 2  of the window  104   a  formed in the case (protection member)  104  and the end face  102   a  of the light guide  102  is determined so that light which is emitted from the light source  101  and reflected by the under face of the light guide  102  is not observed by the viewer  111  who is gazing at the display screen in a direction within a desirable viewing angle range, whereby the undesirable reflected light can be prevented from reaching the viewer&#39;s eye. 
     Furthermore, at the side in which the light source  101  is not provided as shown in FIG. 4A, distance X 1  between the end face  104   a - 1  of the window and the endface  102   a  of the light guide  102  is set to 1.30 mm. At the side in which the light source  101  is provided as shown in FIG. 4B, distance X 2  between the end face  104   a - 2  of the window and the end face  102   a  of the light guide  102  is set to 2.0 mm. In such a structure, light leaking from the end faces 102 a  and 102 c  and light which is emitted from the light source  101  and reflected by the lower face of the light guide  102  can be prevented from reaching the viewer&#39;s eye. 
     In present embodiment, the case  104 , the light guide  102 , and the optical film  105  are positioned so that distances X 1  and X 2  are larger than distances X 3  and X 4 , respectively. However, even in the case where X 1  is equal to X 3 , or X 2  is equal to X 4 , an optical problem does not occur as long as they are equal to or greater than distance X′ or X′″, respectively. This is because only a distance between the end face  104   a - 1  or 104 a - 2  of the case  104  and an end face of the lowest layer of the front light  110  (e.g., the light guide  102  of the FIGS. 4C,  4 D, or the optical film  105  of the FIGS. 4A,  4 B) need to be considered in order to prevent light leakage. 
     However, in the case where an optical film is adhered to the light guide, if the optical film is larger than the light guide, a peripheral portion of the film may be peeled off due to its adhesion accuracy. In the present embodiment, the optical film is attached to the light guide via an adhesive layer (not shown), and the size of the optical film is formed in a size smaller than that of the light guide in order to prevent the optical film from being peeled off in the peripheral portion thereof. Herein, the adhesion accuracy of the optical film is about ±0.5 mm with respect to a reference position. Even if the molding accuracy of the light guide is considered, the size of the light guide becomes larger only by several millimeters with respect to the end face of the optical film. Such an increased size is completely covered within a mounting area of the liquid crystal panel. Therefore, the portability of the liquid crystal display equipment is not spoiled. 
     The values shown above are exemplary values in a configuration wherein an optical film is positioned on the lower face of the light guide. On the other hand, in a configuration wherein an optical film is not provided on the lower face of the light guide, as shown in FIG. 4C, a front light is positioned so that distance X 1  is greater than distance X at a side thereof in which the light source is not provided. On the other hand, at a side in which the light source is provided, as shown in FIG. 4D, the front light is positioned so that distance X 2  is equal to or greater than distance X plus distance a (FIG. 9A) (in this case, X plus α=2×X), in which distance a is provided for preventing light reflected by the light guide  102  from reaching the viewer&#39;s eye. 
     Next, the change in the polarization state of light in the case of employing an optical film composed of a polarizing plate and a quarter-wave plate will be described. 
     In an example shown in FIG. 5, an optical film  105  to be placed on the emission face side of the light guide  102  (FIGS. 4A and 4B) is composed of, from the viewer&#39;s side, a polarizing plate  301  and a quarter-wave plate  302 . The polarizing plate  301  and the quarter-wave plate  302  are combined such that a slow axis (or a fast axis) of the quarter-wave plate  302  makes an angle of about 45° with a transmission axis (or an absorption axis) of the polarizing plate  301 . 
     In the case where light from the light guide  102  or ambient light reaches the optical film  105 , the incident light  300   a  is transmitted through the polarizing plate  301  to be converted into linearly polarized light  300   b  which has an uniform polarization state. The linearly polarized light  300   b  enters the quarter-wave plate  302  and is converted into a circularly polarized light  300   c.    
     In general, the circularly polarized light  300   c  enters the liquid crystal display device and is modulated for displaying images. However, about a 4% of circularly polarized light  300   c  is reflected by a surface of a counter glass substrate  303  which is placed on the viewer&#39;s side of the liquid crystal display device. The reflected light  300   d  is unnecessary light which does not contribute for displaying images, and is a cause for deterioration of the display contrast. 
     However, with the configuration of the polarizing plate  301  and the quarter-wave plate  302  as shown in FIG. 5, the circularly polarized light  300   d  which has been reflected by the surface of the counter glass substrate  303  is converted into circularly polarized light whose phase has been modulated by 180°. Then, the 180°-modulated circularly polarized light  300   d  is converted by the quarter-wave plate  302  into linearly polarized light  300   e  which crosses the transmission axis of the polarizing plate  301  with an angle of 90°. As a result, unnecessary reflected light is removed by the polarizing plate  301 , whereby a reflective type liquid crystal display apparatus in which the contrast does not deteriorate can be obtained. 
     Furthermore, as shown in FIG. 2, in the case where a half-wave plate is inserted between a polarizing plate and a quarter-wave plate of an optical film as described in the present example, the tolerance of the phase delay with respect to the wavelength of the light is compensated for, whereby a circularly polarized state of light can be maintained. As a result, an anti-reflection effect against unnecessary reflected light can be further improved. 
     Furthermore, light leakage from end faces of the optical film which can be found when the liquid crystal display device is observed in an oblique direction, i.e., reflected light which appears around the optical film due to reflected light by the optical film in the direction of the thickness thereof or due to insufficient compensation of the phase, can be prevented by setting distances X 3  and X 4  to be within the above-described ranges, respectively. 
     Table 1 shows relationships between respective viewing angle ranges and minimum values of distances X 1 , X 2 , X 3 , and X 4  for preventing light leakage. Distances X 1  and X 2  each correspond to a structure having no optical film on an emission face of the light guide, while distances X 3  and X 4  each correspond to a structure having an optical film on the emission face of the light guide. 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
               
             
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Relationship between viewing angle range 
               
               
                 &amp; distances X1, X2, X3, and X4 (lower limit) 
               
             
          
           
               
                 Viewing 
                 Front light without 
                 Front light with 
               
               
                 angle range 
                 optical film 
                 optical film 
               
             
          
           
               
                 (deg) 
                 X1 (mm) 
                 X2 (mm) 
                 X3 (mm) 
                 X4 (mm) 
               
               
                   
               
             
          
           
               
                 0 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 10 
                 0.12 
                 0.23 
                 0.17 
                 0.34 
               
               
                 20 
                 0.24 
                 0.47 
                 0.34 
                 0.68 
               
               
                 30 
                 0.36 
                 0.71 
                 0.52 
                 1.04 
               
               
                 40 
                 0.48 
                 0.96 
                 0.70 
                 1.40 
               
               
                 50 
                 0.60 
                 1.20 
                 0.89 
                 1.77 
               
               
                 60 
                 0.71 
                 1.43 
                 1.07 
                 2.13 
               
               
                 70 
                 0.81 
                 1.63 
                 1.23 
                 2.46 
               
               
                 80 
                 0.88 
                 1.76 
                 1.34 
                 2.69 
               
               
                   
               
             
          
           
               
                 Viewing angle range in TABLE 1 is half of an actual 
               
               
                 viewing angle range. 
               
             
          
           
               
                 Light guide: 
                 Thickness td = 1.0 mm 
               
               
                   
                 Refractive index nd = 1.49 
               
               
                 Optical film: 
                 Thickness tk = 0.45 mm 
               
               
                   
                 Refractive index nk = 1.50 
               
             
          
         
       
     
     Distances X 1 , X 2 , X 3 , and X 4  each may be set to a value equal to or greater than a value shown in table 1, according to each viewing angle range which is required by the liquid crystal display apparatus. 
     Furthermore, in the case where there is an input/output device such as a touch panel or the like, or any other component, an air layer, an adhesive layer, etc., at the viewer side of the front light, the position of the end face of the light guide or the end face of the optical film should be determined in consideration of the thickness and the refractive index thereof. 
     For example, FIG. 6 shows an exemplary arrangement in which a touch panel  608  is provided at the viewer&#39;s side of the light guide  607 . The touch panel  608  is composed of, from the viewer&#39;s side, a PET film  602 , a transparent electrode  603 , an air layer  604 , a transparent electrode  605 , and a glass substrate  606 , and serves as an input/output device that converts a change of the electrical resistance or the electrical capacity of transparent electrodes  603  and  605  (provided respective sides of the air layer  604 ) between the contact state and the non-contact state into an electric signal. In FIG. 6, reference numeral  600  denotes a case,  601  denotes an air layer on the front side of the touch panel  608 , and  607  denotes a light guide. 
     In this structure, light incident from the direction of maximum viewing angle θ 1  (light incident from the air layer  601  (1st layer (i=1)) is refracted by the PET film  602  (2nd layer [i=2]), and further refracted by the transparent electrode  603  (3rd layer [i=3]). Furthermore, the light is refracted according to the Snell&#39;s law to reach an end face of the light guide  607  ((g+1)th layer: 7th layer in this example). While traveling from the upper face of the PET film  602  to the lower face of the light guide  607 , the light shifts by distance X 1  in the horizontal direction. Therefore, a component of light which leaks at the end face of the light guide  607  may travel through the same route as that of the incident light but in the opposite direction, and goes out from the upper face of the PET film  602  in the direction of maximum viewing angle θ 1 . 
     Thus, in the case where an input/output device such as a touch panel or a member such as a protecting plate is provided on the front face (viewer&#39;s side) of a light guide, distance X 1  between an end face of the window of the case and an end face of the light guide should be determined in consideration of the thickness and the refractive index of each layer. 
     Furthermore, in the case where an optical film is provided on the lower face of the light guide, distance X 1  should be determined in consideration of the thickness and refractive index of the optical film. 
     For example, FIG. 7 shows an exemplary arrangement in which a touch panel  710  is provided at the viewer&#39;s side of the light guide  707 , and an optical film  708  is provided on the lower face of the light guide  707 . The touch panel  710  is composed of, from the viewer&#39;s side, a PET film  702 , a transparent electrode  703 , an air layer  704 , a transparent electrode  705 , and a glass substrate  706 . In FIG. 7, reference numeral  700  denotes a case,  701  denotes an air layer on the front side of the touch panel  710 , and  707  denotes a light guide. 
     In this structure, light incident from the direction of maximum viewing angle θ 1  (light incident from the air layer  701  (1st layer [k=1]) is refracted by layers from the PET film  702  to the optical film  708  according to the Snell&#39;s law while traveling through these layers, reaching an end face of the optical film  708  ((m+1)th layer: 8th layer in this example). While traveling from the upper face of the PET film  702  to the lower face of the optical film  708 , the light shifts by distance X 3  in the horizontal direction. Therefore, a component of light which leaks at the end face of the optical film  708  may travel through the same route as that of the incident light but in the opposite direction, and goes out from the upper face of the PET film  702  in the direction of maximum viewing angle θ 1 . 
     Thus, in the case where the optical film  708  is provided on the lower surface of the light guide  707 , the thickness and the refractive index of the optical film  708  ((m+1)th layer) is further considered to determine distance X 3  between the end face of the window of the case  700  and the end face of the optical film  708 . 
     This applies to distances X 2  and X 4  between an end face of the window of the case and an end face of the light guide or an end face of the optical film at the side of the front light in which the light source is provided, except that the reflection of light emitted from the light source should be considered. 
     Regarding the above-described touch panel, in the case where the transparent electrode  603 , the transparent electrode  605 , or the air layer  604  is very thin, for example, in the case where each of these layers is as thin as an interference film, the refractive index or the thickness of such a film is negligible. 
     The present invention is not limited to the numeric values shown above. These values may be changed in accordance with the change in the thickness or the refractive index of the light guide or the optical film. Furthermore, in the case where an input/output device (touch panel or the like), protecting plate, etc., are provided to the viewer&#39;s side of the light guide, the thickness and the refractive index thereof should be considered to determine a distance between an end face of a window formed in the case and a corresponding end face of the light guide or the optical film. 
     Furthermore, in the case where a screen of the display apparatus is not square, if the screen size becomes large, or when an aspect ratio (a ratio between a vertical length and a horizontal length) becomes large, a perspective angle may be considerably different between the vertical direction and the horizontal direction. In such a case, the distance between the end face of the window of the case and the end face of the light guide or the optical film may be set separately in the vertical direction and the horizontal direction to different values. 
     In the present embodiment, the optical film is a film composed of a polarizing plate, a half-wave plate, and a quarter-wave plate, but is not limited thereto. A film composed of a polarizing plate and a quarter-wave plate may be alternatively used. In this case also, unnecessary light reflected by a surface of a counter glass substrate of the liquid crystal display device is removed by the polarizing plate and the quarter-wave plate, whereby the contrast of the display can be improved. 
     Furthermore, the optical film may be an anti-reflection film. For example, an anti-reflection film composed of a TAC (triacetylcellulose) film and a dielectric thin film formed thereon, in which a reflection energy is reduced by an interference effect of the thin film. More specifically, on a TAC film, MgF 2  (refractive index: 1.38, thickness: 100 nm) for the first layer, CeF 3  (refractive index: 2.30, thickness: 120 nm) for the second layer, TiO 2  (refractive index: 1.63, thickness: 120 nm) for the third layer, and MgF 2  (refractive index: 1.38, thickness: 100 nm) for the fourth layer are formed by the vacuum evaporation method, thereby fabricating an anti-reflection film which is effective for a wavelength within a broadband. The thickness of this anti-reflection film is 0.11 mm, and the refractive index thereof is 1.50. 
     The material of the light guide is not limited to that described in the present embodiment. The light guide of the present invention may be made of a transparent resin, glass, or the like, by a processing method such as injection molding or the like. The transparent resin may include acrylic resins (polymethylmethacrylate, etc.), polycarbonate resins, epoxy resins, etc. 
     Furthermore, in the present embodiment, the cyclic structure formed on the upper face (viewer&#39;s side) of the light guide consists of a plurality of prisms. Each portion of the cyclic structure is not limited to a prism, but may have a trapezoidal shape, a lenticular shape, a spherical shape, or any other convex/concave shape. 
     In the present embodiment, a 3.9″ reflective type liquid crystal display device is employed, and a viewing angle range up to 40° is considered to determine ok distances X 1  and X 2  between the end face of the window formed in the protection member (case) and the end face of the light guide, and to determine distances X 3  and X 4  between the end face of the window formed in the protection member and the end face of the optical film. However, the present invention is not limited to the values shown in the present embodiment. For example, in a front light having no optical film, distance X 1  may be set to be within the following range:        0   ≦   X1   ≦       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in the air layer of the window (i=1), n 1 =1.00 and θ 1 =80°), and distance X 2  may be set to be within the following range:        0   ≦   X2   ≦       {       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +                (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     On the other hand, in a front light having an optical film, distance X 3  may be set to be within the following range:        0   ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the air layer of the window [k=1], n 1 =1.00 and θ 1 =800), and distance X 4  may be set to be within the following range:        0   ≦   X4   ≦       {       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     For example, in a liquid crystal display device for a large-size screen apparatus which requires a wide viewing angle range, the upper limit of the viewing angle range of the liquid crystal display device, i.e., 80°, is considered to determine the distances X 1 , X 2 , X 3 , and X 4 , in order to prevent unnecessary light leakage. In a liquid crystal display device for a small-size screen apparatus which requires a smaller viewing angle range relative to the large-size screen apparatus, unnecessary light leakage can be prevented as long as the lower limit of the viewing angle range is greater than 0°. 
     As described hereinabove, according to the present invention, at a side of the front light in which the light source is not provided, an end face of a window formed in a protection member (case) is positioned with respect to the light guide such that light incident in a direction within a desirable viewing angle range passes through a lower face of the light guide, whereby light leakage from the end face of the light guide can be prevented. 
     Specifically, distance X 1  between the end face of the window formed in the protection member and the end face of the light guide is set to. be within the following range:        0   ≦   X1   ≦       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in the first layer (i=1), θ 1  is a maximum angle within a desirable viewing angle range), whereby a reflective type liquid crystal display apparatus having a superior display quality can be obtained without spoiling the portability thereof. Preferably, in the first layer(an air layer in the window (i=1), n i =1.00, θ 1  is preferably 80°, and            ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       ≦   X1   ≦       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )                              
     (where, in the first layer (i=1), φ 1  is a desirable perspective angle). Preferably, the perspective angle is smaller than 4°. 
     Furthermore, it is preferable that an optical film is provided on a large face of the light guide which faces. the liquid crystal display device. In such a case, at a side in which the light source is not provided, distance X 3  between the end face of the window formed in the protection member and an end face of the optical film is within the following range:        0   ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the first layer (k=1), θ 1  is a maximum angle within a desirable viewing angle range). Preferably, in the first layer (k=1), n 1 =1.00, and θ 1  is 80°. With such an arrangement, over the viewing angle range from 00° (lower limit) to 80° (upper limit), reflected light which occurs in the direction of the thickness of the optical film and reflected light due to insufficient compensation of a phase by the optical film can be prevented. Therefore, a reflective type liquid crystal display apparatus having a superior display quality can be obtained. Preferably, an end portion of the optical film is covered with the protection member so that distance X 3  is within the following range:            ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       ≦   X3   ≦       ∑     k   =   1     m                     (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )                              
     (where, in the air layer (k=1) of the window, φ 1  is a desirable perspective angle). Preferably, the perspective angle is smaller than 4°. 
     Alternatively, at a side in which the light source is provided, an end face of the window formed in the protection member is positioned with respect to the light guide so that light emitted from the light source and reflected by the lower face of the front light is not observed in a direction within the desirable viewing angle range. Thus, the unnecessary reflected light can be prevented from reaching the viewer&#39;s eye. 
     Specifically, the end portion of the light guide is covered with a protection member such that distance X 2  between the end face of the window formed in the protection member and the end face of the light guide is within the following range:        0   ≦   X2   ≦       {       ∑     i   =   1     g                     (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +                (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     (where, in the first layer (i=1), θ 1  is a maximum angle within a desirable viewing angle range), whereby a reflective liquid crystal display apparatus having a superior display quality can be obtained without spoiling the portability thereof. Preferably, θ 1  is set to 80°, whereby light leakage from the end face of the light guide can be prevented over the viewing angle range from 0° (lower limit) to 800° (upper limit). 
     Furthermore, it is preferable that, at the side in which the light source is provided, the end portion of the light guide is covered with the protection member so that distance X 2  between the end face of the window and the end face of the light guide is set, in accordance with a viewing angle range required for the liquid crystal display device, to be within the following range:              ∑     j   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   ϕ   i       )         )         )       +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   ϕ   g       )         )         )       ≦   X2   ≦       {       ∑     i   =   1     g          (       t     i   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   i     /     n     i   +   1         )        X                 sin                   θ   i       )         )         )       }     +     (       t     g   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   g     /     n     g   +   1         )        X                 sin                   θ   g       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a required perspective angle). 
     The reflective type liquid crystal display apparatus may further include an optical film. In such a case, it is preferable that, at a side in which the light source is provided, the end portion of optical film is covered with the protection member such that distance X 4  between the end face of the window formed in the protection member and the end face of the optical film is within the following range:        0   ≦   X4   ≦       {       ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where, in the first layer (k=1), θ 1  is within adesirable perspective angle range). Preferably, θ 1  is set to 80°, whereby light leakage from the end face of the optical film can be prevented over the viewing angle range from 0° (lower limit) to 800° (upper limit). In addition, light emitted from the light source and reflected by the optical film can be prevented from reaching the viewer&#39;s eye. Thus, a reflective liquid crystal display apparatus having a superior display quality can be obtained. 
     Furthermore, it is preferable that, at the side in which the light source is provided, the end portion of the optical film is covered with the protection member so that distance X 4  between the end face of the window and the end face of the optical film is set, in accordance with a viewing angle range required for the liquid crystal display device, to be within the following range:              ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   ϕ   k       )         )         )       +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   ϕ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   ϕ   m       )         )         )       ≦   X4   ≦       {       ∑     k   =   1     m          (       t     k   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   k     /     n     k   +   1         )        X                 sin                   θ   k       )         )         )       }     +     (       t   m     /     tan        (       90      °     -       sin     -   1            (       (       n     m   -   1       /     n   m       )        X                 sin                   θ     m   -   1         )         )         )     +     (       t     m   +   1       /     tan        (       90      °     -       sin     -   1            (       (       n   m     /     n     m   +   1         )        X                 sin                   θ   m       )         )         )                              
     (where, in the air layer of the window (k=1), φ 1  is a required perspective angle). 
     In the case where an anti-reflection film is employed as the optical film, interference of light emitted from the light source and light reflected by an emission surface of the light guide can be prevented, and light leakage from an end face of the optical film can be prevented. Thus, a reflective liquid crystal display apparatus having a superior display quality can be obtained. 
     In the case where a film composed of a polarizing plate and a quarter-wave plate is employed as the optical film, unnecessary light reflected by the quarter-wave plate or by a surface of a counter glass substrate is removed, whereby contrast deterioration can be prevented. In addition, light leakage from the end face of the optical film can be prevented. Thus, a reflective liquid crystal display apparatus having a superior display quality can be obtained. 
     Alternatively, in the case where a film composed of a polarizing plate, a half-wave plate, and a quarter-wave plate is employed as the optical film, the tolerance of the phase delay with respect to the wavelength of the light is compensated for, whereby a circularly polarized state of light can be maintained. As a result, unnecessary light reflected by the quarter-wave plate or by a surface of a counter glass substrate can be further prevented. Thus, a reflective liquid crystal display apparatus having a superior display quality can be obtained. 
     Furthermore, by employing the reflective type liquid crystal display apparatus according to the present invention which has a superior display quality and a high portability, a small and highly-portable electronic information equipment of low power consumption can be realized. 
     Various other modifications will be apparent to and can be readily made by those skilled in the art without departing from the scope and spirit of this invention. Accordingly, it Is not intended that the scope of the claims appended hereto be limited to the description as set forth herein, but rather that the claims be broadly construed.