Question

The human eye has an approximate angular resolution of $\varphi =5.8\times {10}^{-4}$rad and typical photoprinter prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance z should a printed page be held so that one does not see the individual dots?

• A. 14.5 cm
• B. 20.5 cm
• C. 29.5 cm
• D. 28 cm

Answer 1

The correct option is A 14.5 cm

Here, angular resolution of human eye,
$\varphi =5.8\times {10}^{-4}red$
The linear distance between two successive dots in a typical photo printer is $l=\frac{2.54}{300}cm=0.84\times {10}^{-2}cm.$
At a distance of z cm, the gap distance l will subtend an angle
$\varphi =\frac{l}{z}\therefore z=\frac{l}{\varphi }=\frac{0.84\times {10}^{-2}cm}{5.8\times {10}^{-4}}=14.5cm$