The human eye has an approximate angular resolution of =5.8 10^ -… - Vidyadip

Question

The human eye has an approximate angular resolution of $\phi=5.8\times10^{-4}$ rad and a typical photoprinter prints a minimum of 300dpi (dots per inch, 1inch = 2.54cm). At what minimal distance z should a printed page be held so that one does not see the individual dots.

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Answer

We are given that, angular resolution of human eye $(\phi)=5.8\times10^{-4}$ red.
The printer prints 300 dots per inch.
The linear distance (l) between two dots can be calculated as $\frac{2.54}{300}\text{cm.}$
$=0.84\times10^{-2}\text{cm}$
Now, at a distance of z cm, this subtends an angle, $\phi=\frac{\text{l}}{\text{Z}}$
Substituting $(\phi)=5.8\times10^{-4}\text{ red and }=0.84\times10^{-2}\text{cm}$, we get
$\text{Z}=\frac{0.84\times10^{-2}\text{cm}}{5.8\times10^{-4}}=14.5\text{cm}.$

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