Question
Derive the formula for magnification $m=\frac{v}{u}$ for a spherical lens.
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Answer
→Magnification formed by a spherical lens
$m=\frac{\text { height of the image } h^{\prime}}{\text { height of the object } h}$
Now, from figure 9.56, it is clear that right-angled triangles ABO and A'B'O are similar.
$\therefore \frac{A B}{A^{\prime} B^{\prime}}=\frac{O B}{O B^{\prime}}$
→ As per the New Cartesian sign convention
$\begin{array}{l}\rightarrow AB =+h \\ A^{\prime} B ^{\prime}=-h^{\prime} \\ \therefore \frac{ OB =-h}{- h ^{\prime}}=\frac{-u}{v} \\ \therefore \frac{ hB ^{\prime}=+v}{h}=\frac{v}{u} \\ \text { But } \frac{h^{\prime}}{h}=m \\ \therefore m=\frac{v}{u}\end{array}$
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