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Magnification $M$ is defined as $\frac{-d_i}{d_o}$, where $d_i$ and $d_o$ denote the image distance and object distance, respectively. For a given camera, is the value $M$ typically the same for all values of $d_o$? That is, is it true that $\frac{d_{i_1}}{d_{o_1}} = \frac{d_{i_2}}{d_{o_2}}$ for all $d_{o_1}, d_{o_2}$ where $d_{i_1}$ and $d_{i_2}$ are the corresponding image distances?

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Yes for a given camera with a fixed focus lens, sensor size and sensor to lens distance the optical magnification; $$ M = |{ \frac{ h_{obj} }{h_{img} } }|$$ which is object vertical length divided by its image length on the sensor (a number less than unity, hence a reduction, unless a macro image is taken with a macro lens wihich has a true magnification) will be a constant for most of the proper object distance range.

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  • $\begingroup$ But, given an image and a magnification value, is there a way to work out $h_{img}$? Can pixels in an image be converted to physical height in mm? $\endgroup$ – John M. Oct 21 '17 at 13:47
  • $\begingroup$ yes of course you have to convert pixel size to real world size. $\endgroup$ – Fat32 Oct 21 '17 at 13:50
  • $\begingroup$ But isn't the pixel to mm conversion dependent on the resolution of the display? Can the conversion be done programmatically? $\endgroup$ – John M. Oct 21 '17 at 14:02
  • $\begingroup$ yes and yes. You have a sensor size and total number of pixels (resolution) from which you find the conversion scale factor as $s_f$ mm/pixel $\endgroup$ – Fat32 Oct 21 '17 at 14:18

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