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When an object is placed normallyon the principal axis of a spherial mirror at a distance 'a' from its pole, its image is formed at a distance 'v' from the pole of mirror such that (1)/(v)+(1)/(u)=(1)/(f), where f = focal length of given mirror. The relation is called mirror formula and is true for all types of mirrors under all conditions. However, values of u, v and f must be put with proper signs are per the sign convention followed. If 'h' be the height of the linear object and h' the height of image, then ratio (h')/(h) is called linear magnification or lateral magnification and its value m is given as : m=(h')/(h)=-(v)/(u) (e) Find an expression for longitudinal magnification of a small object placed linearly along the axis of a spherical mirror. |
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Answer» Solution :Let linear size of object be du andlinear size of its image be dv. As per mirror FORMULA, we have `(1)/(v)+(1)/(u)=(1)/(f)` On differentiation, we GET `(-dv)/(v^(2))-(du)/(u^(2))=0` `rArr""(dv)/(v^(2))=-(du)/(u^(2))` `therefore"LONGITUDINAL magnification "=(dv)/(dy)=-(v^(2))/(u^(2))` 
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