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The myth of lateral inversion

Why do so many school textbooks perpetuate the myth of ‘lateral inversion’ when discussing the nature of the image in a plane mirror? Lateral inversion suggests that a mirror has particular properties in one plane only. and so must confuse pupils who wonder why there can be lateral inversion without simultaneous  vertical  inversion.  Some  text  books merely state ’lateral inversion occurs’, but attempt no definition of what this means. Others attempt both statements and explanations, but there is no consensus of interpretation.  The  most  common meaning seems to be something like ’left and right are reversed’, but others refer to the image being ‘back to front’,  and  one  refers  to  a ‘perverted‘ image! It is possible to show that a plane mirror causes no inversion, vertical or lateral. and to expose errors in the  arguments of those  who  attempt o  explain lateral  inversion  as  an  effect  caused by a  plane mirror.  Consider  the  formation of an  image as shown in figure 1. For simplicity. the object is a two-dimensional Cartesian coordinate system. Both object and image lie in planes parallel to the mirror surface. Neither axis is reversed. There is no vertical inversion. There is no lateral inversion. The remaining figures are typical of those found in textbooks which seek to explain lateral inversion and they are included so that misconceptions can be considered. Both figures 2 and 3 consider an object lying in a plane perpendicular to the mirror surface, not parallel to it. Consequently they merely indicate that object points near to a mirror have images near