`text(Transverse or Lateral or Linear Magnification :)`

It is defined as

`m_T=text(height of image)/text(height of object)` `= (h_i)/(h_o)`

After using geometry we get

`m_T=-v/u=f/(f-u)`

Sign of `m_T` states orientation of image with respect to object and its magnitude compares size of image with size of object.

`text(Newtonian formula for mirrors :)`

Here distances are measured from focus

`uv=f^2`

`=>` `m_T=-f/v`

`text(Image for Longitudinal Object :)`

If an object is placed along principal axis then it is called longitudinal object.
If object is of very small size then longitudinal magnification is defined as.

`m_L=text(length of image)/text(length of image)` `=(dv)/(du)`

Now using

`1/v +1/u = 1/f`

Differentiating with respect to u we get

`(dv)/(du)=-(v^2)/(u^2)=-m_T^2`

`=>` `m_L=-m_T^2`