a line scanning , illuminating apparatus for use in an electrophotocopying machine . the apparatus includes a linear source of light , a hyperbolic reflector situated behind the linear light source , and a cylindrical lens located in front of the linear light source . the profile of the reflector is given by the equation : ## equ1 ## wherein the x and y axes intersect at the center line of the reflector , and wherein b is a positive quantity on the x axis representing the distance between the center line of the reflector and a virtual image of the light source created behind the reflector , and wherein a is a negative quantity representing the distance between the center line of the reflector and the linear light source located in front of the reflector .