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Image in Thin Lens Using Formula

Two convex le...

Question

Two convex lens 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 $f_{1} / f_{2}$

A

\frac{m_{1} (1 + m_{1})}{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 B $\frac{m_{1} (1 - m_{2})}{m_{2} (1 - m_{1})}$
$\frac{1}{f_{1}} = \frac{1}{m_{1} u_{1}} - \frac{1}{u_{1}}$
$\frac{1}{f_{2}} = \frac{1}{m_{2} u_{2}} - \frac{1}{u_{2}}$
$∴ f_{1} \times \frac{1}{m_{1} - 1} = f_{2} \times \frac{1}{m_{2} - 1}$
$∴ \frac{f_{1}}{f_{2}} = (\frac{1}{m_{2}} - 1) / (\frac{1}{m_{1}} - 1)$
$= \frac{1 - m_{2}}{1 - m_{1}} \times \frac{m_{1}}{m_{2}}$

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