Abstract:
Disclosed is a light pipe including a body having a hollow therein, and plural prism sections on an outer surface of the body. Each prism section includes a reflection section, a cross section of which is an isosceles right triangle, and an angle adjusting section. The angle adjusting section has a cross section in the shape of a right-angled triangle, a base side of which is an oblique side of the isosceles right triangle. A vertical angle of the right-angled triangle varies with the position of a light source. Installation of the light source at the center of the cross section of the light pipe is not required, thereby increasing the manufacturing efficiency of the light pipe. The light pipe has an internal surface in various shapes including a cylindrical shape to be applicable to various application fields. Power is saved, and light is transmitted to a remote place.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a light pipe, and more particularly to a light pipe using total internal reflection. 
         [0003]    2. Description of the Related Art 
         [0004]    In general, a light pipe is an optical member to transmit light emitted from a light source to a remote plate with relatively low light loss or effectively distribute decorative functional light into a wider area, and includes a light conduit, a light guide, or a light tube. 
         [0005]    The structure of the light pipe is made of a transparent polymer, and the light pipe includes an outer surface having a fine structure and a wall having the shape of a tube having a smooth internal surface opposite to the outer surface. The outer surface includes a plurality of linear prisms having the same shape while extending lengthwise along the light pipe. 
         [0006]    The light pipe allows light ray incident into the light pipe within a predetermined angle to travel through total internal reflection, thereby transmitting the light ray to a remote plate along the inside of the light pipe. 
         [0007]      FIGS. 1 to 3  are views showing a light pipe according to the related art. 
         [0008]      FIG. 1  is a sectional view showing the path of light ray along a cylindrical light pipe employing triangular prisms according to the related art, and  FIG. 2  is an enlarged sectional view showing the path of light ray when the light pipe employing the triangular prisms has an internal flat surface according to the related art.  FIG. 3  is a sectional view showing the range of total reflection in a rectangular-prism-shape light pipe employing the triangular prisms according to the related art. 
         [0009]    Referring to  FIG. 1 , alight source  12  is located at the center of a cross section of a cylindrical light pipe  10  having triangular prisms according to the related art. Light ray  14  emitted from the light source  12  is directed in a radial direction to form an angle of 90° with an internal surface of the cylindrical light pipe  10 . Accordingly, the incident angle of the light ray  14  forms an angle of 0° with a normal line to the internal surface, so that the light ray  14  is not refracted, but introduced into triangular prisms  16 . 
         [0010]    The light ray  14  introduced into the triangular prisms  16  is subject to total internal reflection on a triangular prism surface  18  so that the path of the light ray  14  is changed. The above procedure is repeated, so that light is transmitted with lower light loss along the inside of the cylindrical light pipe  10 . 
         [0011]    If the light source  12  is positioned off the center of the cross section, the total reflection does not occur on the triangular prism surface  18 . Accordingly, a great amount of light ray is emitted to the outside of the light pipe, so that transmission efficiency may be degraded. 
         [0012]    Hereinafter, description will be made regarding the range and the cause in which total reflection does not occur when the light pipe  10  employing the triangular prisms  16  according to the related art has an internal flat surface. 
         [0013]    Referring to  FIG. 2 , when a normal line  22  to an internal surface  20  of the light pipe  10  forms an angle A with the light ray  14  that is incident into the internal surface  20 , an angle B is obtained through Equation 1 under Snell&#39;s Law. In Equation 1, n represents a refractive index of the light pipe  10 . 
         [0000]    
       
         
           
             
               
                 
                   B 
                   = 
                   
                     arcsin 
                     ( 
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         A 
                       
                       n 
                     
                     ) 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0014]    In  FIG. 2 , if an angle P is 90°, an angle D is 135° regardless of the value of A. Accordingly, an angle C formed between a normal line  24  to the triangular prism surface  18  and the light ray  14  is equal to 45°-B. 
         [0015]    In addition, if the refractive index n of the light pipe  10  is about 1.57, a critical angle θ c  becomes 39.56°. Therefore, the light ray  14  is not subject to total reflection, but emitted to the outside if the angle C is 39.56° or less. 
         [0016]    Accordingly, through following Equation 2, if the refractive index of the light pipe  10  is about 1.57, and if the angle A between the normal line  22  to the internal surface  20  of the light pipe  10  and the light lay  14  is about 8.56° or more, the light ray  14  is not subject to total reflection inside the light pipe  10 , but emitted to the outside. 
         [0000]    
       
         
           
             
               
                 
                   
                     45 
                     - 
                     
                       arcsin 
                       ( 
                       
                         
                           sin 
                            
                           
                               
                           
                            
                           A 
                         
                         n 
                       
                       ) 
                     
                   
                   ≤ 
                   39.56 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0017]    Referring to  FIG. 3 , in the case of a rectangular-prism-shape light pipe employing triangular prisms according to the related art, only light ray, which is incident into the internal surface  20  from the light source  12  positioned at the center of the cross section of the light pipe while forming an angle of about 8.56° or less with the normal line  22  to the internal surface  20  of the light pipe, is total-reflected. Accordingly, the total reflection may occur only in sections  26 ,  28 ,  30 , and  32  in which the light ray forms the angle of about 8.56° or less with the normal line  22  to the internal surface  20  of the light pipe. In the remaining sections, the light ray is emitted out of the internal surface  20  like light ray I. Accordingly, if the light pipe employing the triangular prisms according to the related art has an internal flat surface, light ray emitted from a light source  12  is not total-reflected continuously inside the light pipe, but emitted to the outside. 
         [0018]    However, the related art has following problems. 
         [0019]    In other words, if an internal surface of a light pipe has a cylindrical shape, and if a light source is positioned off the center of a cross section of the light pipe, an amount of light traveling through total-reflection on the internal surface of the light pipe is significantly reduced. Accordingly, the position of the light source cannot be freely set. 
         [0020]    In addition, if the internal surface of the light pipe has the shape of a polygonal prism according to the related art, since the range of an incidence angle allowing the light ray emitted from the light source to travel while being total-reflected is narrowed, light cannot be effectively transmitted. 
         [0021]    If a fluorescent signboard according to the related art is employed, a greater amount of light is wasted while being absorbed into a surface sheet to uniformly distribute light of a fluorescent lamp, so that power consumption may be increased. 
       SUMMARY OF THE INVENTION 
       [0022]    Accordingly, the present invention has been made to solve the above-mentioned problems occurring in the prior art. An object of the present invention is to provide a light pipe capable of effectively transmitting light and freely setting the position of a light source. 
         [0023]    Another object of the present invention is to provide alight pipe capable of effectively transmitting light even if the internal surface of the light pipe does not have a cylindrical shape. 
         [0024]    In order to accomplish the above objects, there is provided a light pipe. The light pipe includes a body provided therein with a hollow extending lengthwise along the body, and a plurality of prism sections extending lengthwise along the body on an outer surface of the body. Each prism section includes a reflection section, a cross section of which is an isosceles right triangle, and an angle adjusting section interposed between the body and the reflection section. 
         [0025]    A cross section of the angle adjusting section is a right-angled triangle having an oblique side in contact with the body and a vertical angle interposed between the body and the reflection section in which a size of the vertical angle is determined according to a position of a light source. 
         [0026]    In addition, a cross section of the angle adjusting section is an isosceles triangle that has two sides having a same length in contact with the body and the reflection section and a vertical angle interposed between the body and the reflection section in which a size of the vertical angle is determined according to a position of a light source. 
         [0027]    The size of the vertical is equal to a size of a refracted angle obtained when light ray emitted from the light source travels in parallel to a cross section of the light pipe, is indent into an internal surface of the body, and refracted. 
         [0028]    The vertical angle satisfies an equation, 
         [0000]    
       
         
           
             
               G 
               = 
               
                 arcsin 
                 ( 
                 
                   
                     sin 
                      
                     
                         
                     
                      
                     E 
                   
                   n 
                 
                 ) 
               
             
             , 
           
         
       
     
         [0029]    in which G, n, and E represent the vertical angle, a refractive index of the light pipe, and an incident angle when the light ray emitted from the light source travels in parallel to the cross section of the light pipe and incident into the internal surface of the body, respectively. 
         [0030]    The light pipe further comprises a filter section to transform a color of light emitted from the light source. The filter section includes a reflector to reflect the light ray emitted from the light source, a color filter provided at a front of the reflector, including at least one coloring layer, and having a light transmission property, and a motor to rotate the color filter. 
         [0031]    The hollow has a polygonal shape. 
         [0032]    The prism section satisfies an equation, 
         [0000]        L=h  tan [arcsin( n  sin( G+k )−arcsin( n  sinG)], ( G= 0 , k,  2 k,  3 k , . . . , and  N )
 
         [0033]    In this Case, G Represents the Vertical Angle, L Represents a length of duration in the body having the angle adjusting section with the vertical angle G, h represents a distance between the light source to a point corresponding to an incident angle of 0° into the internal surface of the body, n represents a refractive index of the light pipe, and k is a predetermined positive rational number. 
         [0034]    The hollow has a cylindrical shape. 
         [0035]    The prism section satisfies an equation, 
         [0000]    
       
         
           
             
               L 
               = 
               
                 2 
                  
                 π 
                  
                 
                     
                 
                  
                 
                   r 
                    
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 
                                   arc 
                                    
                                   
                                       
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           rn 
                                            
                                           
                                               
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 G 
                                                 + 
                                                 k 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           r 
                                           - 
                                           h 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                   arcsin 
                                    
                                   
                                     ( 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       
                                         ( 
                                         
                                           G 
                                           + 
                                           k 
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               360 
                             
                             - 
                           
                         
                       
                       
                         
                           
                             
                               
                                 arcsin 
                                  
                                 
                                   ( 
                                   
                                     
                                       rn 
                                        
                                       
                                           
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       G 
                                     
                                     
                                       r 
                                       - 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 arcsin 
                                  
                                 
                                   ( 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     G 
                                   
                                   ) 
                                 
                               
                             
                             360 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
 
             
              
             
               ( 
               
                 
                   G 
                   = 
                   0 
                 
                 , 
                 k 
                 , 
                 
                   2 
                    
                   k 
                 
                 , 
                 
                   3 
                    
                   k 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 
                   and 
                    
                   
                       
                   
                    
                   N 
                 
               
               ) 
             
           
         
       
     
         [0036]    In this case, G represents the vertical angle, L represents a length of duration in the body having the angle adjusting section with the vertical angle G, r represents a radius of a cross section of the hollow, n represents a refractive index of the light pipe, k is a predetermined positive rational number, and h represents a distance between the light source to a point corresponding to an incident angle of 0° onto the internal surface of the body. 
         [0037]    A cross section of the hollow is a figure formed by combining two same circular arcs to each other. 
         [0038]    The prism section satisfies an equation, 
         [0000]    
       
         
           
             
               L 
               = 
               
                 2 
                  
                 π 
                  
                 
                     
                 
                  
                 
                   r 
                    
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 
                                   arc 
                                    
                                   
                                       
                                   
                                    
                                   
                                     sin 
                                      
                                     
                                       ( 
                                       
                                         
                                           rn 
                                            
                                           
                                               
                                           
                                            
                                           
                                             sin 
                                              
                                             
                                               ( 
                                               
                                                 G 
                                                 + 
                                                 k 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           r 
                                           - 
                                           h 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 - 
                                 
                                   arcsin 
                                    
                                   
                                     ( 
                                     
                                       n 
                                        
                                       
                                           
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       
                                         ( 
                                         
                                           G 
                                           + 
                                           k 
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                               360 
                             
                             - 
                           
                         
                       
                       
                         
                           
                             
                               
                                 arcsin 
                                  
                                 
                                   ( 
                                   
                                     
                                       rn 
                                        
                                       
                                           
                                       
                                        
                                       sin 
                                        
                                       
                                           
                                       
                                        
                                       G 
                                     
                                     
                                       r 
                                       - 
                                       h 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 arcsin 
                                  
                                 
                                   ( 
                                   
                                     n 
                                      
                                     
                                         
                                     
                                      
                                     sin 
                                      
                                     
                                         
                                     
                                      
                                     G 
                                   
                                   ) 
                                 
                               
                             
                             360 
                           
                         
                       
                     
                     ) 
                   
                 
               
             
             , 
             
               
 
             
              
             
               ( 
               
                 
                   G 
                   = 
                   0 
                 
                 , 
                 k 
                 , 
                 
                   2 
                    
                   k 
                 
                 , 
                 
                   3 
                    
                   k 
                 
                 , 
                 … 
                  
                 
                     
                 
                 , 
                 
                   and 
                    
                   
                       
                   
                    
                   N 
                 
               
               ) 
             
           
         
       
     
         [0039]    In this case, G represents the vertical angle, L represents a length of duration in the body having the angle adjusting section with the vertical angle G, r represents a radius of the circular arc, n represents a refractive index of the light pipe, k is a predetermined positive rational number, and h represents a distance between the light source to a point corresponding to an incident angle of 0° onto the internal surface of the body. 
         [0040]    A cross section of the hollow is a figure formed by combining two same circular arcs facing each other and two same straight lines facing each other. 
         [0041]    As described above, the light pipe according to the present invention has the following effects. 
         [0042]    In other words, when the internal surface of the light pipe has a cylindrical shape, even if the light source is positioned off the center of the cross section of the light pipe, the light ray can travel while being total-reflected from the internal surface of the light pipe. Accordingly, it is possible to overcome a limitation that the light source must be installed at the center of the cross section of the light pipe. Therefore, the manufacturing efficiency of the light pipe can be increased. 
         [0043]    According to the present invention, the internal surface of the light pipe can have various shapes as well as a cylindrical shape in a conventional technology, so that the light pipe can be used in various application fields such as a signboard and various displays. Accordingly, electric power can be saved, and light can be effectively transmitted to a remote place. 
         [0044]    In addition, the present invention can provide a light pipe that can be used for a signboard and various displays to which a conventional cylindrical light pipe cannot be applied. Particularly, when a rectangular prism-shape-light pipe is used in a fluorescent signboard, the electric power saving efficiency and the manufacturing efficiency can be increased. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0045]      FIG. 1  is a sectional view showing the path of light ray along a cylindrical light pipe employing triangular prisms according to the related art; 
           [0046]      FIG. 2  is an enlarged sectional view showing the path of light ray when the light pipe employing the triangular prisms has an internal flat surface according to the related art; 
           [0047]      FIG. 3  is a sectional view showing the range of total reflection in a rectangular-prism-shape light pipe employing the triangular prisms according to the related art; 
           [0048]      FIG. 4  is an enlarged sectional view showing the path of light ray along a light pipe employing a prism section according to one embodiment of the present invention; 
           [0049]      FIG. 5  is an enlarged sectional view showing the path of light ray along a light pipe employing a prism section according to another embodiment of the present invention; 
           [0050]      FIG. 6  is an enlarged sectional view showing the path of light ray of a light pipe employing a prism formed by tilting a conventional triangular prism at a predetermined angle; 
           [0051]      FIG. 7  is a perspective view showing the light pipe according to the first embodiment of the present invention; 
           [0052]      FIG. 8  is a sectional view showing the light pipe according to the first embodiment of the present invention; 
           [0053]      FIG. 9  is a sectional view showing the path of light ray along the light pipe according to the first embodiment of the present invention; 
           [0054]      FIG. 10A  is a perspective view showing the light ray traveling inside the light pipe according to the first embodiment of the present invention; 
           [0055]      FIG. 10B  is a perspective view showing the light ray traveling in a prism section of the light pipe according to the first embodiment of the present invention; 
           [0056]      FIG. 10C  is a longitudinal sectional view showing the light ray, which travels in the prism section of the light pipe according to the first embodiment of the present invention, on a YZ plane; 
           [0057]      FIG. 10D  is a cross sectional view showing the light ray, which travels in the prism section of the light pipe according to the first embodiment of the present invention, on a ZX plane; 
           [0058]      FIG. 11  is a perspective view showing the light pipe according to a second embodiment of the present invention; 
           [0059]      FIG. 12  is a sectional view showing the light pipe according to the second embodiment of the present invention; 
           [0060]      FIG. 13  is a sectional view showing the path of light ray in the light pipe according to the second embodiment of the present invention; 
           [0061]      FIG. 14  is a perspective view showing a light pipe according to a third embodiment of the present invention; 
           [0062]      FIG. 15  is a sectional view showing the light pipe according to the third embodiment of the present invention; 
           [0063]      FIG. 16  is a sectional view showing the path of light ray in the light pipe according to the third embodiment of the present invention; 
           [0064]      FIG. 17  is a perspective view showing a light pipe according to a fourth embodiment of the present invention; 
           [0065]      FIG. 18  is a sectional view showing the light pipe according to the fourth embodiment of the present invention; and 
           [0066]      FIG. 19  is an exploded perspective view showing the structure of a light pipe according to a fifth embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0067]    Hereinafter, a light pipe according to an exemplary embodiment of the present invention will be described in detail with reference to accompanying drawings. 
         [0068]      FIGS. 4 to 19  are views showing a light pipe according to embodiments of the present invention. 
         [0069]    In the following specification, an incident angle refers to an angle between an incident light ray and a boundary surface with a first medium when the light ray traveling into a second medium reaches the boundary surface with the first medium. A refracted angle refers to an angle between light ray refracted from the boundary surface and a normal line to the boundary surface. 
         [0070]    Hereinafter, the structure of the light pipe according to embodiments of the present invention will be described with reference to  FIGS. 4 and 6 . 
         [0071]      FIG. 4  is an enlarged sectional view showing the path of light ray along a light pipe employing a prism section according to one embodiment of the present invention, and  FIG. 5  is an enlarged sectional view showing the path of light ray along a light pipe employing a prism section according to another embodiment of the present invention.  FIG. 6  is an enlarged sectional view showing the path of light ray of a light pipe employing a prism section formed by tilting a conventional triangular prism at a predetermined angle. 
         [0072]    As shown in  FIG. 4 , a light pipe  50  according to an embodiment of the present invention includes a body  52  and a prism section  54 . 
         [0073]    The body  52  is prepared in the form of a hollow tube in which a hollow  56  extends lengthwise along the body  52 , and constitutes an inner part of the light pipe  52 . A plurality of prism sections  54  are formed lengthwise along an outer surface of the body  52 . 
         [0074]    In this case, the prism section  54  has a rectangular cross section, and includes a reflection section  58  and an angle adjusting section  60 . 
         [0075]    In this case, the reflection section  58  corresponds to an isosceles right triangle when the cross section of the prism section  54  is divided into two right-angled triangles. In other words, the reflection section  58  has a shape obtained by tilting a triangular prism provided in a light pipe according to the related art by a predetermined angle. 
         [0076]    In addition, the angle adjusting section  60  is interposed between the body  52  and the reflection section  58 . The cross section of the angle adjusting section  60  is a right-angled triangle, and an oblique side of the right-angled triangle comes into contact with the body  52 . The size of a vertical angle between the body  52  and the reflection section  58  varies depending on the position of a light source. 
         [0077]    Hereinafter, detailed description will be made regarding the structure of the prism section  54  when light ray  62  emitted from the light source is incident into an internal surface  64  of the body  52  at an incident angle E. 
         [0078]    If the light ray  62  emitted from the light source (not shown) forms an angle, that is, the incident angle E with a normal line  65  to the internal surface  64  of the body  52 , a refracted angle G is obtained through Equation 3 under Snell&#39;s Law. In Equation 3, n represents a refractive index of the light pipe. 
         [0000]    
       
         
           
             
               
                 
                   G 
                   = 
                   
                     arcsin 
                      
                     
                       ( 
                       
                         
                           sin 
                            
                           
                               
                           
                            
                           E 
                         
                         n 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0079]    In this case, an angle H between a normal line  67  to a prism surface  66  of the prism section  54  and the light ray  62  must be greater than a critical angle so that the light ray  62  is total-reflected on the prism surface  66 . Accordingly, the condition of total reflection is represented as following Equation 4. 
         [0000]    
       
         
           
             
               
                 
                   H 
                   &gt; 
                   
                     arcsin 
                      
                     
                       ( 
                       
                         1 
                         n 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0080]    After the light ray  62  has been total-reflected on the prism surface  66 , the light ray  62  is again total-reflected on an adjacent prism surface  68  of the prism section  54  to travel through the hollow  56  of the light pipe  50 . To cause total reflection on the adjacent prism surface  68 , the light ray  62  must be incident into the adjacent prism surface  68  at an angle greater than the critical angle. 
         [0081]    Accordingly, the angle H between the normal line  66  to the prism surface  66  and the light ray  62  is preferably 45° in order to total-reflect the light ray  62  on the prism surface  66 , and then again total-reflect the light ray  62  on the adjacent prism surface  68 . 
         [0082]    If the angle H is 45°, the refractive index of polycarbonate, poly (methyl methacrylate), acryl, poly propylene, or poly styrene, poly (vinyl chloride) of the light pipe  50  according to an embodiment of the present invention satisfies Equation 4. 
         [0083]    Since the cross section of the reflection section  58  is an isosceles right triangle, an angle formed between the cross section of the reflection section  58  and the cross section of the body  52  is equal to the refracted angle G at which the light ray  62  is refracted from the internal surface  64  of the body  52 . In other words, the shape of the reflection section  58  corresponds to a shape obtained by tilting a structure having a cross section in the shape of an isosceles right triangle by the angle G. 
         [0084]    Meanwhile, the angle G formed between the cross section of the reflection section  58  and the cross section of the body  52  is equal to the size of a vertical angle of the cross section of the angle adjusting section  60 . In other words, the angle adjusting section  60  is interposed between the body  52  and the reflection section  58 , and the vertical angle between the body  52  and the reflection section  58  in the cross section of the angle adjusting section  60  is equal to a refracted angle when the light ray  62  is incident into the internal surface  64  of the body  52  and refracted. Accordingly, the shape of the angle adjusting section  60  varies depending on the relative position between the light source and the internal surface  64  of the light pipe  50 . 
         [0085]    When the incident angle E of the light ray  62  has a value in the range of 0° to 90°, the refracted angle G has a value in the range of 0° to the critical angle. Accordingly, the vertical angle of the right-angled triangle corresponding to the cross section of the angle adjusting section  60  has the range represented in Equation 5. 
         [0000]    
       
         
           
             
               
                 
                   0 
                   &lt; 
                   G 
                   &lt; 
                   
                     arcsin 
                      
                     
                       ( 
                       
                         1 
                         n 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   5 
                 
               
             
           
         
       
     
         [0086]    Meanwhile, as the prism section  54  is designed in small size, the transmission efficiency of light may be increased, and the weight of the light pipe  50  may reduced. 
         [0087]    The light pipe  50  including the prism section  54  may be made of materials, such as polycarbonate, poly (methyl methacrylate), acryl, poly propylene, poly styrene, or poly (vinyl chloride), representing superior light transmittance or mechanical stability. 
         [0088]    The material of the light pipe  50  may be determined according to the type of a used light source. For example, if the light source of the light pipe  50  is a point light source, such as a mercury lamp or a metallic lamp, representing high efficiency, polycarbonate having strong heat resistance may be used as a material of the light pipe  50  when taking into consideration the temperature of heat emitted from the light source. 
         [0089]    As shown in  FIG. 5 , a light pipe  70  according to another embodiment of the present invention includes a body  72  and a prism section  74 . 
         [0090]    The body  72  is prepared in the form of a hollow tube in which a hollow  56  extends lengthwise along the body  72 , and constitutes an inner part of the light pipe  70 . A plurality of prism sections  74  are formed lengthwise along an outer surface of the body  72 . 
         [0091]    In this case, the prism section  74  has a rectangular cross section, and includes a reflection section  78  and an angle adjusting section  80 . 
         [0092]    In this case, the reflection section  78  corresponds to an isosceles right triangle when the cross section of the prism section  74  is divided into two isosceles triangles. In other words, the reflection section  58  has a shape obtained by tilting a triangular prism provided in a light pipe according to the related art by a predetermined angle. 
         [0093]    In addition, the angle adjusting section  80  is interposed between the body  72  and the reflection section  78 , and the cross section of the angle adjusting section  80  is configured as an isosceles triangle having a vertical angle determined according to the position of the light source. In other words, the cross section of the angle adjusting section  80  is an isosceles triangle in which two sides of the isosceles triangle make contact with the body  72  and the reflection section  78  and have the same length, and a vertical angle of the isosceles triangle is interposed between the body  72  and the reflection section  78  and determined according to the position of the light source. 
         [0094]    Hereinafter, detail description will be made regarding the structure of the prism section  74  while taking into consideration a casein which light ray  82  emitted from the light source is indent onto an internal surface  84  of the body  72  at an incident angle E. 
         [0095]    If an angle formed between the light ray  82  emitted from the light source (not shown) and a normal line  85  to the internal surface  84  of the body  72 , that is, an incident angle is E, a refracted angle G is obtained through Equation 3 under Snell&#39;s Law. In Equation 3, n represents the refractive index of the light pipe  70 . 
         [0096]    To enable the light ray  82  to be total-reflected from a prism surface  86  of the prism section  74 , an angle H formed between the normal line  87  of the prism surface  86  and the light ray  82  must be greater than a critical angle. Accordingly, the condition of total reflection is represented through Equation 4. 
         [0097]    After the light ray  82  has been total-reflected from the prism surface  86 , the light ray  82  is again total-reflected from an adjacent prism surface  88  of the prism section  74  and directed to the hollow  76  of the light pipe  70 . In this case, similarly, the light ray  82  must be incident into the adjacent prism surface  88  at an incident angle greater than the critical angle such that the total reflection again occurs on the prism surface  88 . 
         [0098]    Accordingly, the angle H formed between the normal line  87  to the prism surface  86  and the light ray  82  is preferably 45° such that the light ray  82  is total-reflected from the prism surface  88  and again total-reflected from the adjacent prism surface  88 . 
         [0099]    If the angle H is 45°, the refractive index n of polycarbonate, poly (methyl methacrylate), acryl, poly propylene, or poly styrene, poly (vinyl chloride) of the light pipe  70  according to another embodiment of the present invention satisfies Equation 4. 
         [0100]    Since the cross section of the reflection section  88  is an isosceles right triangle, an angle formed between the cross section of the reflection section  78  and the cross section of the body  72  is equal to the refracted angle G at which the light ray  82  is refracted from the internal surface  84  of the body  72 . In other words, the shape of the reflection section  88  corresponds to a shape obtained by tilting a structure having a cross section in the shape of an isosceles right triangle by the angle G. 
         [0101]    Meanwhile, the angle G formed between the cross section of the reflection section  78  and the cross section of the body  72  is equal to the size of a vertical angle the cross section of the angle adjusting section  80 . In other words, the angle adjusting section  80  is interposed between the body  72  and the reflection section  78 , and the vertical angle between the body  72  and the reflection section  78  in the cross section of the angle adjusting section  80  is equal to a refracted angle when the light ray  82  is incident into the internal surface  84  of the body  72  and refracted. Accordingly, the shape of the angle adjusting section  80  varies depending on the relative position between the light source and the internal surface  84  of the light pipe  70 . 
         [0102]    When the incident angle E of the light ray  82  has a value in the range of 0° to 90°, the refracted angle G has a value in the range of 0° to the critical angle. Accordingly, the vertical angle of the isosceles triangle corresponding to the cross section of the angle adjusting section  80  has the range represented in Equation 5. 
         [0103]    Meanwhile, as the prism section  74  is designed in small size, the transmission efficiency of light may be increased, and the weight of the light pipe  70  may reduced. 
         [0104]    The light pipe  70  including the prism section  74  may be made of materials, such as polycarbonate, poly(methyl methacrylate), acryl, poly propylene, poly styrene, or poly(vinyl chloride), representing superior light transmission or mechanical stability. 
         [0105]    The material of the light pipe  70  may be determined according to the type of a used light source. For example, if the light source of the light pipe  70  is a point light source, such as mercury lamp or metallic lamp having high efficiency, polycarbonate having strong heat resistance may be used as a material of the light pipe  70  when taking into consideration the temperature of heat emitted from the light source. 
         [0106]      FIG. 6  is an enlarged sectional view showing the path of light ray of a light pipe employing a prism formed by tilting a conventional triangular prism at a predetermined angle. 
         [0107]    Referring to  FIG. 6 , when a prism  92  applied to a light pipe  90  has a shape obtained by tilting a conventional triangular prism by a predetermined angle, if light ray  94  emitted from a light source (not shown) and incident into the light pipe  90  is primarily total-reflected from an extension section  96  of the conventional triangular prism, the light ray is not continuously total-reflected, but is emitted to the outside. 
         [0108]    Accordingly, the prism section  54  or  74  according to an embodiment of the present invention has a rectangular cross section without the section  96 , and is formed by combining the reflection section  58  or  78  having a cross section in the shape of an isosceles right triangle depending on the relative position between the light source and the internal surface  64  or  84  of the light pipe  50  or  70  with the angle adjusting section  60  or  80  having a cross section in the shape of a right-angled triangle or an isosceles triangle, so that the total reflection can continuously occur. 
         [0109]    Hereinafter, the structure of a light pipe according to a first embodiment of the present invention will be described with respect to  FIGS. 7 to 10 . 
         [0110]      FIG. 7  is a perspective view showing the light pipe according to the first embodiment of the present invention, and  FIG. 8  is a sectional view showing the light pipe according to the first embodiment of the present invention.  FIG. 9  is a sectional view showing the path of light ray along the light pipe according to the first embodiment of the present invention.  FIG. 10A  is a perspective view showing the light ray traveling inside the light pipe according to the first embodiment of the present invention, and  FIG. 10B  is a perspective view showing the light ray traveling in a prism section of the light pipe according to the first embodiment of the present invention.  FIG. 10C  is a longitudinal sectional view showing the light ray, which travels in the prism section of the light pipe according to the first embodiment of the present invention, on a YZ plane.  FIG. 10D  is a cross sectional view showing the light ray, which travels in the prism section of the light pipe according to the first embodiment of the present invention, on a ZX plane. 
         [0111]      FIGS. 8 and 9  are sectional views showing the light pipe according to the first embodiment of the present invention, in which only the light components of a light ray parallel to a cross section of the light pipe traveling in the light pipe are illustrated. 
         [0112]    Referring to  FIG. 7 , a light pipe  100  according to a first embodiment of the present invention includes a body  102  and a prism section  104 . The body  102  is prepared in the form of a hollow tube in which a hollow  106  extends lengthwise along the body  102 . A plurality of prism sections  104  are formed lengthwise along an outer surface of the body  102 . Each prism section  104  includes a reflection section  112  and an angle adjusting section  114 . 
         [0113]    The light ray  110 , which has been emitted from a light source  108  and incident into the hollow  106  of the light pipe  100 , is incident into an internal surface  116  of the light pipe  100  and then total-reflected from the prism section  104  under a total-reflection condition according to Snell&#39;s Law. The procedure is repeated, so that the light ray  110  travels lengthwise along the light pipe  100 . 
         [0114]    In addition, since the hollow  106  of the light pipe  100  is filled with air, the light ray  110  can travel lengthwise along the light pipe  100  without transmission loss. 
         [0115]    The light pipe  100  according to the first embodiment of the present invention is different from a conventional light pipe in that the hollow  106  of the light pipe  100  has the shape of a rectangular prism. 
         [0116]    Meanwhile, in the light pipe  100  according to the first embodiment of the present invention, the shape of the prism section  104  varies according to the relative position between the internal surface  116  of the body  102  of the light pipe  100  and the light source  108 . 
         [0117]    The size of a vertical angle between the body  102  and the reflection section  112  in a right angle triangle that corresponds to a cross section of the angle adjusting section  114  constituting the prism section  104  is identical to the size of a refracted angle obtained when the light ray  110  incident into the internal surface  116  of the body  102  while traveling in parallel to the cross section of the light pipe  100  is refracted. The refracted angle of the light ray  110  is determined according to the refractive index of the light pipe  100  and the incident angle of the light ray  110 , and the size of the incident angle varies according to the relative position between the light source  108  and the internal surface  116  of the body  102 . 
         [0118]    Hereinafter, the shape of the prism section  104  varying according to the relative position between the light source  108  and the internal surface  116  of the body  102  will be described in detail with reference to  FIG. 8 . 
         [0119]    An incident angle E corresponding to a refracted angle G of 0°, 1°, 2°, 3°, . . . and N° can be calculated by using the refractive index n of the light pipe  100 . In addition, a distance M from a point where the incident angle of the light ray is 0° to a point where the incident angle of the light ray is E can be obtained by using a distance h between the light source  108  and the point where the incident angle of the light ray incident into the internal surface  116  of the body  102  is 0°. On the assumption that a refracted angle is defined as Gin the duration between a point where the refracted angle is G and a point where a refracted angle is G+1°, a length L of the duration having the refracted angle G can be obtained by using the distance M. 
         [0120]    In this case, since the size of a vertical angle between the body  102  and the reflection section  112  in the cross section of the angle adjusting section  114  is equal to the refracted angle G of the light ray  110 , the length L of the duration at which the vertical angle is G may be expressed as a generalized formula. The procedure to find the duration length L is expressed through following Equation 6. 
         [0000]      sin E=n sin G 
         [0000]      E=arcsin(n sin G) 
         [0000]      M=h tan E 
         [0000]      M=h tan [arcsin(n sin G)], (G=0, 1, 2, 3, . . . , and N) 
         [0000]        L=h  tan [arcsin( n  sin( G+ 1)−arcsin( n  sinG)], ( G= 0, 1, 2, 3, and  N )  Equation 6
 
         [0121]    Although the present invention has been described about a case in which G is 0°, 1°, 2°, 3°, . . . and N°, on the assumption that k is a positive rational number, the length L of the duration at which the vertical angle is G when the refracted angle G is increased by k° may be expressed as a generalized formula, and expressed through Equation 7. 
         [0000]        L=h  tan [arcsin( n  sin( G+k )−arcsin( n  sin  G )], ( G= 0 , k,  2 k , 3 k , . . . , and  N )  Equation 7
 
         [0122]    Meanwhile, for Example, if the Refractive Index N of the Light pipe  100  according to the first embodiment of the present invention is 1.57, and the refracted angle G is 0°, 1°, 2° and N° the incident angle E, the length M, and the duration length L have result values shown in Table 1. 
         [0000]    
       
         
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Refracted angle G 
                 Incident angle E 
                   
                 Duration 
               
               
                 (unit °) 
                 (unit °) 
                 Distance M 
                 length L 
               
               
                   
               
             
             
               
                  0 
                 0   
                 0 
                 0.027 h 
               
               
                  1 
                  1.57 
                 0.027 h 
                 0.028 h 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                  5 
                  7.86 
                 0.138 h 
                 0.028 h 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 10 
                 15.82 
                 0.283 h 
                 0.031 h 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 15 
                 23.97 
                 0.445 h 
                 0.035 h 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 20 
                 32.48 
                 0.636 h 
                 0.044 h 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                 . 
                 . 
                 . 
                 . 
               
               
                   
               
             
          
         
       
     
         [0123]    As described above, in the light pipe  100  according to the first embodiment of the present invention, the size of the vertical angle between the body  102  and the reflection section  112  in the right-angled triangle that is the cross section of the angle adjusting section  114  is determined by using both the refractive index n of the light pipe  100  and the distance h between the light source  108  and the internal surface  116  of the body  102 . Accordingly, when the cross section of the hollow  106  of the light pipe  100  has a polygonal shape, the calculation procedure is identically applied. 
         [0124]    Meanwhile, in the light pipe  100  according to the first embodiment of the present invention, when the light source  108  is positioned at the center of the cross section of the hollow  106 , prism sections  104  are arranged in the same form on two facing surfaces of the light pipe  100 . In addition, if the cross section of the hollow  106  has a square shape, and the light source  108  is positioned at the center of the cross section of the hollow  106 , prism sections  104  are arranged in the same form on four surfaces of the light pipe  100 . 
         [0125]    In contrast, if the light source  108  is positioned off the center of the cross section of the hollow  106 , the arrangement of the prism sections  104  on the four surfaces of the light pipe  100  varies depending on the distance h from the light source  108  to the internal surface  116  of the body  102 . 
         [0126]    Hereinafter, the path of the light lay  110  in the light pipe  100  according to the first embodiment of the present invention will be described with reference to  FIG. 9 . 
         [0127]    As shown in  FIG. 9 , the light ray  110  emitted from the light source  108  is incident into the light pipe  100  and total reflected from the prism section  104  under a total-reflection condition according to Snell&#39;s Law. The light ray  110  that has been total-reflected from the prism section  104  is incident into an opposite prism section  104  at the same incident angle and again total reflected from the opposite prism section  104 , such that the light ray  110  travels lengthwise along the light pipe  100 . 
         [0128]    In other words, after the light ray  110  has been total reflected from the first incident surface, the light ray  110  is incident into a surface facing the first incident surface or a surface adjacent to the first incident surface at the same incident angle as that onto the first incident surface, such that total reflection occurs again. Accordingly, the light ray  110  travels lengthwise along the light pipe  100  while being continuously total-reflected from the prism sections  104 . 
         [0129]    Hereinafter, an allowance range for total reflection when the light ray  110  emitted from the light source  108  travels while forming a predetermined angel with a central line  118  of the light pipe  100  will be described with reference to  FIGS. 10A to 10D . 
         [0130]    Referring to  FIG. 10A , when the light ray  110  travels while forming an angle Z with the central line  118  of the light pipe  100 , if the angle Z is 90°, the incident angle of the light ray  110  on a prism surface of the prism section  104  is 45°. 
         [0131]    Meanwhile, referring to  FIG. 10B , when the angle Z approximates 0°, the light ray  110  is incident while traveling in substantially parallel to a longitudinal direction of the prism section  104 . The light ray  110  is refracted from the internal surface  116  of the body  102  of the light pipe  100  so that the light ray  110  forms an angle T with respect to the prism surface of the prism section  104 . 
         [0132]    Referring to  FIGS. 10C and 10D , since the light ray  110  is incident into the light pipe  100  at an incident angle of about 90° on a ZY plane, the refracted angle P is approximately equal to the critical angle. Accordingly, when only a ZY component of the light ray  110  is analyzed on the ZY plane, the refracted angle P of the light ray  110  can be found according to Snell&#39;s Law, an angle Q between the prism surface and the light ray  110  can be found by using the refracted angle P. The refracted angel P and the angel of Q are found through Equation 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                     = 
                     
                       arcsin 
                        
                       
                         ( 
                         
                           1 
                           n 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Q 
                     = 
                     
                       90 
                       - 
                       
                         arcsin 
                          
                         
                           ( 
                           
                             1 
                             n 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0133]    In addition, when only a ZX component of the light ray  110  is analyzed on the ZX plane, the light ray  110  forms an angle of 45° with the prism surface. 
         [0134]    In this case, if the angle Q is 90°, the angle T in  FIG. 10B  is identical to the angel of 45° in  FIG. 10D . In addition, if the angle Q is 0°, the angle T in  FIG. 10B  is always 0° regardless of the angle of 45° in  FIG. 10D . Accordingly, the angle T is proportional to the angle Q. Accordingly, the angle T and an incident angle H of the light ray  110  onto the prism surface can be found through Equation 9. 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     = 
                     
                       
                         
                           45 
                            
                           Q 
                         
                         90 
                       
                       = 
                       
                         
                           1 
                           2 
                         
                          
                         Q 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     T 
                     = 
                     
                       
                         1 
                         2 
                       
                        
                       
                         [ 
                         
                           90 
                           - 
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 1 
                                 n 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     H 
                     = 
                     
                       90 
                       - 
                       T 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     H 
                     = 
                     
                       
                         90 
                         - 
                         
                           
                             1 
                             2 
                           
                            
                           
                             [ 
                             
                               90 
                               - 
                               
                                 arcsin 
                                  
                                 
                                   ( 
                                   
                                     1 
                                     n 
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                       
                       = 
                       
                         45 
                         + 
                         
                           
                             1 
                             2 
                           
                            
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 1 
                                 n 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
         [0135]    Meanwhile, an angle Z between the light ray  110  and the central line  118  of the light pipe  100  is within the range of 0° to 90°. As described above, if the angle Z is 90°, the incident angle H is 45. If the angle Z 0°, the incident angle H can be found through Equation 9. Accordingly, if the angle Z is within the range of 0° to 90°, the range of the incident angle H is identical to that shown in Equation 10, and this satisfies the condition of total reflection as shown in  FIG. 10 . 
         [0000]    
       
         
           
             
               
                 
                   
                     45 
                      
                     H 
                      
                     
                       45 
                       + 
                       
                         
                           1 
                           2 
                         
                          
                         
                           arcsin 
                            
                           
                             ( 
                             
                               1 
                               n 
                             
                             ) 
                           
                         
                          
                         
                           ( 
                           
                             0 
                              
                             z 
                              
                             90 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     H 
                     &gt; 
                     
                       arcsin 
                        
                       
                         ( 
                         
                           1 
                           n 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   10 
                 
               
             
           
         
       
     
         [0136]    In this case, the n is a refractive index according to the material of the light pipe  100 . The incident angle H satisfies Equation 10 with respect to polycarbonate, poly(methyl methacrylate), acryl, poly propylene, poly styrene, or poly(vinyl chloride) that is a material of the light pipe  100 . 
         [0137]    Accordingly, in the light pipe  100  according to the first embodiment of the present invention, since the angle Z satisfies the range of 0° to 90°, all light rays  110  emitted from the light source  108  satisfies the total-reflection condition. 
         [0138]    If the n is 1.57, since the incident angle H of the light ray  110  onto the prism surface of the prism section  104  exists between 45° and 64.78°, the incident angle H satisfies the total-reflection condition, that is, H&gt;39.56°. 
         [0139]    In addition, although the calculation procedure is not performed through the equations as described above, if the angle Z is 90°, the incident angle H may have the minimum value. As the angle Z is reduced, the incident angle H is gradually increased. Accordingly, if the incident angle H satisfies the total-reflection condition when the angle Z is 90°, the light ray  110  satisfies the total-reflection condition at all points of the prism section  104 . 
         [0140]    Hereinafter, the structure of a light pipe according to a second embodiment of the present invention will be described with reference to  FIGS. 11 to 13 . 
         [0141]      FIG. 11  is a perspective view showing the light pipe according to the second embodiment of the present invention, and  FIG. 12  is a sectional view showing the light pipe according to the second embodiment of the present invention.  FIG. 13  is a sectional view showing the path of light ray in the light pipe according to the second embodiment of the present invention. 
         [0142]    In this case,  FIGS. 12 and 13  are sectional views showing the light pipe according to the second embodiment of the present invention, and show only components of a light ray parallel to a cross section of the light pipe traveling in the light pipe. 
         [0143]    Referring to  FIG. 11 , a light pipe  200  according to the second embodiment of the present invention has the shape of a cylindrical hollow tube, and includes a body  202  and a prism section  204 . The body  202  is prepared in the form of a hollow tube in which a hollow  206  extends lengthwise along the body  202 . A plurality of prism sections  204  are formed lengthwise along an outer surface of the body  202 . The prism section  204  includes a reflection section  212  and an angle adjusting section  214 . 
         [0144]    After light ray  210  has been emitted from the light source  208  and incident into the hollow  206  of the light pipe  200 , the light ray  210  is incident into an internal surface  216  of the light pipe  200  and total-reflected from the prism section  204  under a total-reflection condition according to Snell&#39;s Law. The above procedure is repeated, so that the light ray  210  travels lengthwise along the light pipe  200 . 
         [0145]    Since the hollow  206  of the light pipe  200  is filled with air, the light ray  210  can travel lengthwise along the light pipe  200  without transmission loss. 
         [0146]    The light pipe  200  according to the second embodiment of the present invention is different from the conventional light pipe in that the light source  208  is positioned off the center of a cross section of the light pipe  200 . 
         [0147]    Meanwhile, in the light pipe  200  according to the second embodiment of the present invention, the shape of the prism section  204  varies according to the relative position between the light source  208  and the light pipe  200 . 
         [0148]    The size of a vertical angle between the body  202  and the reflection section  212  in a right-angled triangle that is a cross section of an angle adjusting section  214  constituting the prism section  204  is equal to the size of a refracted angle obtained when the light ray  210  incident into the internal surface  216  of the body  202  while traveling in parallel to the cross section of the light pipe  200  is refracted. The refracted angle of the light ray  210  varies according to the refractive index of the light pipe  200  and an incident angle of the light ray  210 . The size of the incident angle varies according to a relative position between the light source  208  and the internal surface  216  of the body section  202 . 
         [0149]    Hereinafter, the shape of the prism section  204  varying according to the relative position between the light source  208  and the internal surface  216  of the body section  202  will be described in detail with reference to  FIG. 12 . 
         [0150]    When the refracted angle G is 0°, 1°, 2°, 3°, . . . and N° the incident angle E can be found by using the refractive index n. In addition, the length M of an arc between a point corresponding to the incident angle of 0° onto the internal surface  216  of the body  202  and a point corresponding to the incident angle E can be found by using a distance h between the light source  208  and the point corresponding to the incident angle of 0°, a radius r of the cross section of the hollow  206 , a distance s between the light source  208  and a point corresponding to the incident angle E, an angle C between a line linking the light source  208  with the point corresponding to the incident angle of 0° and a line linking the light source  208  with the point corresponding to the incident angle E, and an angle D between a line linking a center of a circle, which is the shape of the cross section of the hollow  206 , with the point corresponding to the incident angle of 0° and a line linking the center of the circle with the point corresponding to the incident angle E. In addition, on the assumption that a refracted angel is defined as G in the duration between a point where the refracted angle is G and a point where a refracted angle is G+1°, the length L of the duration having the refracted angle G can be obtained by using the length M of the arc. 
         [0151]    In this case, since the size of a vertical angle between the body  202  and the reflection section  212  in a right-angled triangle, which is a cross section of the angle adjusting section  214 , is equal to the refracted angle G of the light ray  210 , the length L of a duration in which the vertical angle is the refracted angle G may be expressed as a generalized formula. The procedure to find the length L is expressed through following Equation 11. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       sin 
                        
                       
                           
                       
                        
                       E 
                     
                     = 
                     
                       n 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       G 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     E 
                     = 
                     
                       
                         C 
                         - 
                         D 
                       
                       = 
                       
                         arcsin 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             n 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             G 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       s 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       C 
                     
                     = 
                     
                       r 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       D 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       s 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       E 
                     
                     = 
                     
                       
                         ( 
                         
                           r 
                           - 
                           h 
                         
                         ) 
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       D 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     C 
                     = 
                     
                       arcsin 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             r 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             E 
                           
                           
                             r 
                             - 
                             h 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     D 
                     = 
                     
                       C 
                       - 
                       
                         ( 
                         
                           C 
                           - 
                           D 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     D 
                     = 
                     
                       
                         arcsin 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             
                               rn 
                                
                               
                                   
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               G 
                             
                             
                               r 
                               - 
                               h 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         arcsin 
                          
                         
                           ( 
                           
                             n 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             G 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     M 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         r 
                          
                         
                           ( 
                           
                             D 
                             360 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     M 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       r 
                        
                       
                         
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 
                                   rn 
                                    
                                   
                                       
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   G 
                                 
                                 
                                   r 
                                   - 
                                   h 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 G 
                               
                               ) 
                             
                           
                         
                         360 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       L 
                       = 
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           r 
                           ( 
                           
                               
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               arc 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       rn 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             G 
                                                             + 
                                                             1 
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     
                                                       r 
                                                       - 
                                                       h 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           
                                             arcsin 
                                             ( 
                                             
                                               n 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     G 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                              
                                             
                                                 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     360 
                                   
                                   - 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           
                                             rn 
                                              
                                             
                                                 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             G 
                                           
                                           
                                             r 
                                             - 
                                             h 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           n 
                                            
                                           
                                               
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           G 
                                         
                                         ) 
                                       
                                     
                                   
                                   360 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       G 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     3 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       and 
                        
                       
                           
                       
                        
                       N 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
         [0152]    Although the present invention has been described about a case in G is 0°, 1°, 2°, 3°, . . . and N°, on the assumption that k is a positive rational number, the length L of the duration at which the vertical angle is the refracted angle G when the refracted angle G is increased by k° may be expressed as a generalized formula, and expressed through Equation 12. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         r 
                          
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               arc 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       rn 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             G 
                                                             + 
                                                             k 
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     
                                                       r 
                                                       - 
                                                       h 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           
                                             arcsin 
                                              
                                             
                                               ( 
                                               
                                                 n 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 
                                                   ( 
                                                   
                                                     G 
                                                     + 
                                                     k 
                                                   
                                                   ) 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     360 
                                   
                                   - 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           
                                             rn 
                                              
                                             
                                                 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             G 
                                           
                                           
                                             r 
                                             - 
                                             h 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           n 
                                            
                                           
                                               
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           G 
                                         
                                         ) 
                                       
                                     
                                   
                                   360 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     G 
                     = 
                     0 
                   
                   , 
                   k 
                   , 
                   
                     2 
                      
                     k 
                   
                   , 
                   
                     3 
                      
                     k 
                   
                   , 
                   … 
                    
                   
                       
                   
                   , 
                   
                     and 
                      
                     
                         
                     
                      
                     N 
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
         [0153]    As described above, in the light pipe  200  according to the second embodiment of the present invention, the shape of the prism section  204  varies according to the refractive index n, a distance h between the light source  208  and a point where an incident angle onto the internal surface  216  of the body  202  is 0°, and a radius r of the cross section of the hollow  206 . 
         [0154]    Hereinafter, the path of the light ray  210  in the light pipe  200  according to the second embodiment of the present invention will be described with reference to  FIG. 13 . 
         [0155]    As shown in  FIG. 13 , the light ray  210  emitted from the light source  208  is incident into the light pipe  200  and reflected from prism section  204  under a total-reflection condition according to Snell&#39;s Law. The light ray  210  that has been total-reflected from the prism section  204  is again total-reflected from an opposite prism section  204  at the same angle, so that the light ray  210  travels lengthwise along the light pipe  200 . 
         [0156]    After the light ray  210  has been total-reflected from the first incident surface, the light ray  210  is incident into an incident surface opposite to the first incident surface at an incident angle the same as that of the first incident surface and again total reflected. Accordingly, the light ray  210  is continuously total-reflected from the prism section  204  while traveling lengthwise along the light pipe  200 . 
         [0157]    Meanwhile, in the light pipe  200  according to the second embodiment of the present invention, if the light ray  210  travels while forming an angle of 90°, and an incident angle onto the prism section  204  satisfies the total-reflection condition, the light ray  210  satisfies the total-reflection condition at all points of the prism section  204  similarly to the case of the light pipe  100  according to the first embodiment of the present invention described with reference to  FIG. 10 . 
         [0158]    Hereinafter, the structure of the light pipe  300  having a hollow employing a figure, which is formed by combining two circular arcs with each other, as a cross section according to a third embodiment of the present invention will be described with reference to  FIGS. 14 to 16 . 
         [0159]      FIG. 14  is a perspective view showing a light pipe  300  according to the third embodiment of the present invention, and  FIG. 15  is a sectional view showing the light pipe  300  according to the third embodiment of the present invention.  FIG. 16  is a sectional view showing the path of light ray  310  in the light pipe  300  according to the third embodiment of the present invention. 
         [0160]    In this case,  FIGS. 15 and 16  are sectional views showing the light pipe  300  according to the third embodiment of the present invention, and show only components of light ray parallel to across section of the light pipe traveling in the light pipe. 
         [0161]    Referring to  FIG. 14 , the light pipe  300  according to the first embodiment of the present invention includes a body  302  and a prism section  304 . The body  102  is prepared in the form of a hollow tube in which a hollow  306  extends lengthwise along the body  102 . The hollow  306  has the cross section in the shape of a figure formed by combining two same circular arcs with each other. 
         [0162]    A plurality of prism sections  304  are formed lengthwise along an outer surface of the body  302 . Each prism section  304  includes a reflection section  312  and an angle adjusting section  314 . 
         [0163]    The light ray  310  emitted from a light source  308  is total-reflected from the prism section  304  according to Snell&#39;s Law, and the above procedure is repeated, so that the light ray  310  travels lengthwise along the light pipe  300 . Since the hollow  306  of the light pipe  300  is filled with air, the light ray  310  can travel without transmission loss. 
         [0164]    The light pipe  300  according to the third embodiment of the present invention is different from the conventional light pipe in that the cross section of the hollow  306  has the shape of a figure formed by combining two same circular arcs. 
         [0165]    Meanwhile, in the light pipe  300  according to the third embodiment of the present invention, the shape of the prism section  304  varies according to the relative position between the light source  308  and the light pipe  300 . 
         [0166]    The vertical angle between the body  302  and the reflection section  312  in a right-angled triangle that is a cross section of an angle adjusting section  314  constituting the prism section  304  is equal to the refracted angle of the light ray  310 , which is obtained when the light ray  310  incident into the internal surface  316  of the body  302  while traveling in parallel to the cross section of the light pipe  300  is refracted. The refracted angle of the light ray  310  varies according to a refractive index of the light pipe  300  and an incident angle of the light ray  310 . The size of the incident angle varies according to a relative position between the light source  308  and the internal surface  316  of the body section  302 . 
         [0167]    Hereinafter, the shape of the prism section  304  varying according to the relative position between the light source  308  and the internal surface  316  of the body  302  will be described with reference to  FIG. 15 . 
         [0168]    When the refracted angle G is 0°, 1°, 2°, 3°, . . . and N° the incident angle E can be found by using the refractive index n of the light pipe  300 . In addition, the length M of an arc between a point corresponding to the incident angle of 0° onto the internal surface  316  of the body  302  and a point corresponding to the incident angle E can be found by using a distance h between the light source  308  and the point corresponding to the incident angle of 0°, a curvature radius r of an arc constituting the cross section of the hollow  306 , a distance s between the light source  308  and the point corresponding to the incident angle E, an angle C between a line linking the light source  308  with the point corresponding to the incident angle of 0° and a line linking the light source  308  with the point corresponding to the incident angle E, and an angle D between a line linking a curvature center of an arc constituting the cross section of the hollow  306  with the point corresponding to the incident angle of 0° and a line linking the curvature center with the point corresponding to the incident angle E. In addition, on the assumption a refracted angle is G in duration between a point where the refracted angle is G and a point wherein the refracted angle is G+1°, the length L of the duration having the refracted angle G can be obtained by using the length M of the arc. 
         [0169]    In this case, since the size of a vertical angle between the body  302  and the reflection section  312  in a right-angled triangle, which is a cross section of the angle adjusting section  314 , is equal to the refracted angle G of the light ray  310 , the length L of a duration at which the vertical angle is equal to the refracted angle G may be expressed as a generalized formula. The procedure to find the length L is expressed through following Equation 13. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       sin 
                        
                       
                           
                       
                        
                       E 
                     
                     = 
                     
                       n 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       G 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     E 
                     = 
                     
                       
                         C 
                         - 
                         D 
                       
                       = 
                       
                         arcsin 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             n 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             G 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       s 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       C 
                     
                     = 
                     
                       r 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       D 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       s 
                        
                       
                           
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       E 
                     
                     = 
                     
                       
                         ( 
                         
                           r 
                           - 
                           h 
                         
                         ) 
                       
                        
                       sin 
                        
                       
                           
                       
                        
                       D 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     C 
                     = 
                     
                       arcsin 
                        
                       
                           
                       
                        
                       
                         ( 
                         
                           
                             r 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             E 
                           
                           
                             r 
                             - 
                             h 
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     D 
                     = 
                     
                       C 
                       - 
                       
                         ( 
                         
                           C 
                           - 
                           D 
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     D 
                     = 
                     
                       
                         arcsin 
                          
                         
                             
                         
                          
                         
                           ( 
                           
                             
                               rn 
                                
                               
                                   
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               G 
                             
                             
                               r 
                               - 
                               h 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         arcsin 
                          
                         
                           ( 
                           
                             n 
                              
                             
                                 
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             G 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     M 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         r 
                          
                         
                           ( 
                           
                             D 
                             360 
                           
                           ) 
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     M 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       r 
                        
                       
                         
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 
                                   rn 
                                    
                                   
                                       
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   G 
                                 
                                 
                                   r 
                                   - 
                                   h 
                                 
                               
                               ) 
                             
                           
                           - 
                           
                             arcsin 
                              
                             
                               ( 
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 sin 
                                  
                                 
                                     
                                 
                                  
                                 G 
                               
                               ) 
                             
                           
                         
                         360 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       L 
                       = 
                       
                         2 
                          
                         π 
                          
                         
                             
                         
                          
                         
                           r 
                           ( 
                           
                               
                           
                            
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               arc 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       rn 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             G 
                                                             + 
                                                             1 
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     
                                                       r 
                                                       - 
                                                       h 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           
                                             arcsin 
                                             ( 
                                             
                                               n 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     G 
                                                     + 
                                                     1 
                                                   
                                                   ) 
                                                 
                                               
                                             
                                              
                                             
                                                 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     360 
                                   
                                   - 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           
                                             rn 
                                              
                                             
                                                 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
                                             G 
                                           
                                           
                                             r 
                                             - 
                                             h 
                                           
                                         
                                         ) 
                                       
                                     
                                     - 
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           n 
                                            
                                           
                                               
                                           
                                            
                                           sin 
                                            
                                           
                                               
                                           
                                            
                                           G 
                                         
                                         ) 
                                       
                                     
                                   
                                   360 
                                 
                               
                             
                           
                           ) 
                         
                       
                     
                     , 
                     
                       
 
                     
                      
                     
                       G 
                       = 
                       0 
                     
                     , 
                     1 
                     , 
                     2 
                     , 
                     3 
                     , 
                     … 
                      
                     
                         
                     
                     , 
                     
                       and 
                        
                       
                           
                       
                        
                       N 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
         [0170]    Although the present invention has been described about a case in G is 0°, 1°, 2°, 3°, . . . and N° on the assumption that k is a positive rational number, the length L of the duration at which the vertical angle is the refracted angle G when the refracted angle G is increased by k° may be induced to a generalized formula, and expressed through Equation 14. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     = 
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         r 
                          
                         
                           ( 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                             
                                               arc 
                                                
                                               
                                                   
                                               
                                                
                                               
                                                 sin 
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       rn 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         sin 
                                                          
                                                         
                                                           ( 
                                                           
                                                             G 
                                                             + 
                                                             k 
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     
                                                       r 
                                                       - 
                                                       h 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                             - 
                                           
                                         
                                       
                                       
                                         
                                           
                                             arcsin 
                                              
                                             
                                               ( 
                                               
                                                 n 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 sin 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 
                                                   ( 
                                                   
                                                     G 
                                                     + 
                                                     k 
                                                   
                                                   ) 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     360 
                                   
                                   - 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       arcsin 
                                        
                                       
                                         ( 
                                         
                                           
                                             rn 
                                              
                                             
                                                 
                                             
                                              
                                             sin 
                                              
                                             
                                                 
                                             
                                              
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         [0171]    As described above, in the light pipe  300  according to the third embodiment of the present invention, the shape of the prism section  304  varies according to the refractive index n, a distance h between the light source  308  and the point where an incident angle onto the internal surface  316  of the body  302  is 0°, and the curvature radius r of the arc constituting the cross section of the hollow  306 . 
         [0172]    Hereinafter, the path of the light ray  310  in the light pipe  300  according to the third embodiment of the present invention will be described with reference to  FIG. 16 . 
         [0173]    As shown in  FIG. 16 , the light ray  310  emitted from the light source  308  is incident into the light pipe  300  and reflected from prism section  304  under a total-reflection condition according to Snell&#39;s Law. The light ray  310  that has been total-reflected from the prism section  304  is again total-reflected from an opposite prism section  304  at the same angle, so that the light ray  310  travels lengthwise along the light pipe  300 . 
         [0174]    After the light ray  310  has been total-reflected from the first incident surface, the light ray  310  is incident into an incident surface opposite to the first incident surface at an incident angle the same as that of the first incident surface and again total reflected. Accordingly, the light ray  310  is continuously total-reflected from the prism section  304  while traveling lengthwise along the light pipe  300 . 
         [0175]    Meanwhile, in the light pipe  300  according to the third embodiment of the present invention, if the light ray  310  travels while forming an angle of 90°, and an incident angle onto the prism section  304  satisfies the total-reflection condition, the light ray  310  satisfies the total-reflection condition at all points of the prism section  304  similarly to the case of the light pipe  100  according to the first embodiment of the present invention described with reference to  FIG. 10 . 
         [0176]    Hereinafter, the structure of the light pipe  400  having a hollow employing a figure, which is formed by combining two same circular facing each other and two same straight lines facing each other, as a cross section according to a third embodiment of the present invention will be described with reference to  FIGS. 17 to 18 . 
         [0177]      FIG. 17  is a perspective view showing the light pipe  400  according to the fourth embodiment of the present invention, and  FIG. 18  is a sectional view showing the light pipe  400  according to the fourth embodiment of the present invention. 
         [0178]    In this case,  FIG. 18  is a sectional view showing the light pipe  400  according to the fourth embodiment of the present invention, and show only components of light ray parallel to a cross section of the light pipe  400  traveling in the light pipe  400 . 
         [0179]    Referring to  FIG. 17 , the light pipe  400  according to the fourth embodiment of the present invention includes a body  402  and the prism section  404 . The body  402  includes a hollow  406  formed through the light pipe  400  lengthwise along the light pipe  400 . The cross section of the hollow  406  has a shape of a figure formed by combining two same circular arcs facing each other and two same straight lines facing each other. 
         [0180]    A plurality of prism sections  404  are provided on an outer surface of the body  402 , and each prism section  404  includes a reflection section  412  and an angle adjusting section  414 . 
         [0181]    The light ray  410  emitted from the light source  408  is total-reflected from the prism sections  404  under a total-reflection condition according to Snell&#39;s Law. Through the above procedure, the light ray  410  travels lengthwise along the light pipe  400 . In addition, since the hollow  406  of the light pipe  400  is filled with air, the light ray  410  can travel without light loss. 
         [0182]    The light pipe  400  according to the fourth embodiment of the present invention is different from the conventional light pipe in that the cross section of the hollow  406  has the shape of a figure formed by combining two same circular arcs facing each other and two same straight lines facing each other. 
         [0183]    Meanwhile, in the light pipe  400  according to the fourth embodiment of the present invention, the shape of each prism section  404  varies according to the relative position between the light source  408  and the light pipe  400 . 
         [0184]    The size of a vertical angle between the body  402  and the reflection section  412  in a right-angled triangle that is a cross section of an angle adjusting section  414  constituting the prism section  404  is equal to the size of a refracted angle of the light ray  410  obtained when the light ray  410  incident into the internal surface  416  of the body  402  while traveling in parallel to the cross section of the light pipe  400  is refracted. The refracted angle of the light ray  410  varies according to a refractive index of the light pipe  400  and an incident angle of the light ray  410 . The size of the incident angle varies according to a relative position between the light source  408  and the internal surface  416  of the body section  402 . 
         [0185]    Meanwhile, the shape of the prism section  404  varying according to the relative position between the light source  408  and the internal surface  416  of the body  402  are separately determined in a straight-line portion of the cross section of the hollow  406  and a circular-arc-portion of the cross section. 
         [0186]    In other words, in the straight-line portion of the cross section of the hollow  406 , the shape of the prism section  404  is determined through Equation 7 as shown in  FIG. 8  similarly to the light pipe according to the first embodiment of the present invention. In the circular-arc-portion of the cross section of the hollow  406 , the shape of the prism section  404  is determined through Equation 14 as shown in  FIG. 15  similarly to the light pipe according to the third embodiment of the present invention. 
         [0187]    Hereinafter, the path of the light ray  410  in the light pipe  400  according to the fourth embodiment of the present invention will be described with reference to  FIG. 18 . 
         [0188]    As shown in  FIG. 18 , the light ray  410  emitted from the light source  408  is incident into the light pipe  400  and reflected from prism section  404  under a total-reflection condition according to Snell&#39;s Law. The light ray  410  that has been total-reflected from the prism section  404  is again total-reflected from an opposite prism section  404  at the same incident angle, so that the light ray  410  travels lengthwise along the light pipe  400 . 
         [0189]    After the light ray  410  has been total-reflected from the first incident surface, the light ray  410  is incident into an incident surface opposite to the first incident surface at an incident angle the same as that of the first incident surface and again total reflected. Accordingly, the light ray  410  is continuously total-reflected from the prism section  404  while traveling lengthwise along the light pipe  400 . 
         [0190]    Meanwhile, in the light pipe  400  according to the third embodiment of the present invention, if the light ray  410  travels while forming an angle of 90°, and an incident angle onto the prism section  404  satisfies the total-reflection condition, the light ray  410  satisfies the total-reflection condition at all points of the prism section  404  similarly to the case of the light pipe  100  according to the first embodiment of the present invention described with reference to  FIG. 10 . 
         [0191]    When the light pipe  400  according to the fourth embodiment of the present invention is employed for a signboard, the light pipe  400  can be reduced in size and represent a superior outer appearance. 
         [0192]    Meanwhile, although only the case in which the cross section of the angle adjusting section  114 ,  214 ,  314 , or  414  has the shape of a right-angled triangle has been considered in the first to fourth embodiments of the present invention, the cross section of the angle adjusting section  114 ,  214 ,  314 , or  414  may have the shape of an isosceles triangle as shown in  FIG. 5 . In this case, the size of the isosceles triangle constituting the cross section of the angle adjusting section  114 ,  214 ,  314 , or  414  is equal to a refracted angle obtained when the light ray  110 ,  210 ,  310 , or  410  incident into the internal surface  116 ,  216 ,  316 , or  416  of the body  102 ,  202 ,  302 , or  402  while traveling in parallel to the cross section of the light pipe  100 ,  200 ,  300 , or  400  is refracted. Accordingly, the light ray  110 ,  210 ,  310 , or  410  is continuously total-reflected while traveling lengthwise along the light pipe  100 ,  200 ,  300 , or  400 . 
         [0193]    Hereinafter, the structure of a light pipe  500  according to a fifth embodiment of the present invention will be described with reference to  FIG. 19 . 
         [0194]      FIG. 19  is an exploded perspective view showing the structure of the light pipe  500  according to the fifth embodiment of the present invention. 
         [0195]    As shown in  FIG. 19 , the light pipe  500  according to the fifth embodiment of the present invention further includes a filter section  520  in addition to components of the light pipe according to the first embodiment to the fourth embodiment of the present invention. The filter section  520  transforms a color of light emitted from a light source  508 . 
         [0196]    The filter section  520  further includes a reflector  522  to reflect light ray emitted from the light source  508 . The reflector  522  is positioned at one end of the light pipe  500  to reflect the light ray emitted from the light source  508  toward an opposite end of the light pipe  500 . 
         [0197]    In addition, the filter section  520  includes a color filter  524 . The color filter  524  is provided at the front of the reflector  522 , and includes at least one coloring layer  526 . The color of light incident into the color filter  524  is changed when the light passes through the coloring layer  526 . 
         [0198]    The color filter  524  is a circular glass plate, and includes a dichroic filter which has been subject to dichroic coating, colored glass, or polycarbonate according to the use of the light pipe  500 . For example, when taking into consideration the heat emitted from the light source  508  of the light pipe  500 , the color filter  524  includes the dichroic filter which has been subject to the dichroic coating. 
         [0199]    In addition, the filter section  520  includes a motor  528  to rotate the color filter  524 . The motor  528  is used to convert the color of the light emitted to the outside of the light pipe  500  by rotating the color filter  524 . 
         [0200]    When the light pipe  500  according to the fifth embodiment of the present invention is used for a signboard or various displays, the light pipe  500  can be used as a device to covert white light emitted from the light source  508  into various color light. In other words, the light ray emitted from the light source  508  is transmitted into the color filter  524 , so that the light pipe  500  can discharge various color light to the outside. 
         [0201]    Since a prism section is arranged in parallel to the light pipe according to each embodiment of the present invention, the light pipe can be mass-produced through extrusion molding based on polycarbonate or acrylic resin, and the thickness of the light pipe can be determined within the range sufficient to maintain the shape of the light pipe and endure external shock according to the material characteristics of the light pipe. 
         [0202]    When the light pipe according to each embodiment of the present invention is used for a signboard or a display, light must be uniformly emitted from the surface of the light pipe. When the light pipe has a short length, the light can be uniformly emitted from the surface of the light pipe. However, when the light pipe has a long length, the internal or external surface of the light pipe must be treated to be rough, or a light diffusion film is attached to the internal or external surface of the light pipe, so that total-reflected light can be emitted to the outside of the pipe. 
         [0203]    Although the exemplary embodiments of the present invention have been described, it is understood that the present invention should not be limited to these exemplary embodiments but various changes and modifications can be made by one ordinary skilled in the art within the spirit and scope of the present invention as hereinafter claimed.