Ray optics
Question

# A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. Find the focal length of the eye- piece

Moderate
Solution

## When final image is at infinity the magnification produced by eye piece is                      $\left(\frac{{\mathrm{u}}_{0}}{{\mathrm{v}}_{\mathrm{o}}}+1\right)=\frac{\left(6.5-{\mathrm{f}}_{\mathrm{e}}\right)}{0.5}$Overall magnification  $\frac{{\mathrm{v}}_{0}}{{\mathrm{u}}_{\mathrm{o}}}\left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)=100$                                            $\frac{{\mathrm{v}}_{\mathrm{o}}}{{\mathrm{u}}_{\mathrm{o}}}=4{\mathrm{f}}_{\mathrm{e}}$                                    $\left(4{\mathrm{f}}_{\mathrm{e}}+1\right)=2\left(6.5-{\mathrm{f}}_{\mathrm{e}}\right)$                                      $4{\mathrm{f}}_{\mathrm{e}}+1=13-2{\mathrm{f}}_{\mathrm{e}}$                                            $6{\mathrm{f}}_{\mathrm{e}}=12$                                             ${\mathrm{f}}_{\mathrm{e}}=2\mathrm{cm}$

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