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The sum of the reciprocals of object distance and image distance is equal to what? why?

A formula which gives the relationship between image distance (v),object distance(u) and focal length (f) of a spherical mirror is known as the mirror formula.The mirror formula can be written as :
1/Image distance + 1/Object distance = 1/Focal length
or 1/v + 1/u = 1/f
where v = distance of image from mirror
          u = distance of object from mirror
and     f  = focal length of the mirror


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