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Magnification by Thin Lenses

Two convex le...

Question

Two convex lenses of focal lengths $f_{1}$ and $f_{2}$ form images with magnification $m_{1}$ and $m_{2}$ , when used individually for an object kept at the same distance from the lenses. Then $f_{1} / f_{2}$ is:

A

\frac{m_{1} (1 + m_{2})}{m_{2} (1 + m_{2})}

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B

\frac{m_{1} (1 + m_{2})}{m_{2} (1 + m_{1})}

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C

\frac{m_{2} (1 + m_{1})}{m_{1} (1 + m_{2})}

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D

\frac{m_{2} (1 + m_{2})}{m_{1} (1 + m_{1})}

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Solution

The correct option is A $\frac{m_{1} (1 + m_{2})}{m_{2} (1 + m_{1})}$
Len's formula with magnification is:
$\frac{1 + m_{1}}{m_{1}} = \frac{- u}{f_{1}} \frac{1 + m_{2}}{m_{2}} = \frac{- u}{f_{2}} \Rightarrow \frac{\frac{1 + m_{2}}{m_{2}}}{\frac{1 + m_{1}}{m_{1}}} = \frac{f_{1}}{f_{2}} = \frac{m_{1}}{m_{2}} (\frac{1 + m_{2}}{1 + m_{1}})$

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