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A students plots a graph between inverse of magnification $1 / m$ produced by a convex thin lens and the object distance $u$ as shown in figure. What was the focal length of the lens used?
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The correct answer is:
$\frac{c}{b}$
Lens formula, $\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}$
or $\frac{\mathrm{u}}{\mathrm{v}}-1=\frac{\mathrm{u}}{\mathrm{f}}$ $\Rightarrow \frac{1}{\mathrm{~m}}-1=\frac{\mathrm{u}}{\mathrm{f}}$ or $\frac{1}{\mathrm{~m}}=\left(\frac{1}{\mathrm{f}}\right) \mathrm{u}+1$
this is the equation of a straight line whose slope
$\frac{1}{f}-\frac{b}{c} \therefore 1-\frac{c}{b}$
or $\frac{\mathrm{u}}{\mathrm{v}}-1=\frac{\mathrm{u}}{\mathrm{f}}$ $\Rightarrow \frac{1}{\mathrm{~m}}-1=\frac{\mathrm{u}}{\mathrm{f}}$ or $\frac{1}{\mathrm{~m}}=\left(\frac{1}{\mathrm{f}}\right) \mathrm{u}+1$
this is the equation of a straight line whose slope
$\frac{1}{f}-\frac{b}{c} \therefore 1-\frac{c}{b}$
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