Question

The human eye has an approximate angular resolution of $\phi=5.08 \times 10^{-4} rad$ and typical photoprinter prints a minimum of $360$ dpi (dots per inch, $1$ inch $=2.54\, cm$ ). At what minimum distance, $Z$ (in $cm$ ) should a printed page be held so that one does not see the individual dots?

Answer 1

Here, angular resolution of human eye, $\phi=5.08 \times 10^{-4} rad$
The linear distance between two successive dots in a typical photoprinter is
$l=\frac{2.54}{360} cm$
At a distance of $Z cm$, the gap distance $l$ will subtend an angle,
$\phi=\frac{l}{Z}$
$\therefore Z =\frac{l}{\phi}$
$=\frac{2.54 \times 10^{-2}}{360 \times 5.08 \times 10^{-4}}$
$=13.89\, cm$