# Problem: An object and its lens-produced real image are 2.4 m apart. If the lens has 55-cm focal length, what are the possible values for the object distance and magnification?

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###### FREE Expert Solution

Lens equation:
$\overline{)\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{o}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbit{s}}_{\mathbit{i}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbit{f}}}$

Magnification:

$\overline{){\mathbf{m}}{\mathbf{=}}\frac{{\mathbf{h}}_{\mathbf{i}}}{{\mathbf{h}}_{\mathbf{o}}}{\mathbf{=}}{\mathbf{-}}\frac{{\mathbf{s}}_{\mathbf{i}}}{{\mathbf{s}}_{\mathbf{o}}}}$

The separation between the object and the image is 2.4m

Therefore, so + si = 2.4

si = 2.4 - so

Substituting to the lens equation:

1/so + 1/(2.4 - so) = 1/(55 × 10-2)

###### Problem Details

An object and its lens-produced real image are 2.4 m apart. If the lens has 55-cm focal length, what are the possible values for the object distance and magnification?