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Question: The human eye has an approximate angular resolution of \(\varphi = 5.8 \times 10^{- 4}\)rad and typi...

The human eye has an approximate angular resolution of φ=5.8×10−4\varphi = 5.8 \times 10^{- 4}rad and typical photoprinter prints a minimum of 300 dpi (dots per inch, 1 inch= 2.54cm). 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

14.5 cm

Explanation

Solution

Here angular resolution of human eye,

φ=5.8×10−4rad\varphi = 5.8 \times 10^{- 4}rad

The linear distance between to successive dots in a typical photo printer is

l=2.54300cm=0.84×10−2cml = \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

φ=1zF∴zF=1φ=0.84×10−2cm5.8×10−4=14.5cm\varphi = \frac{1}{z_{F}}\therefore z_{F} = \frac{1}{\varphi} = \frac{0.84 \times 10^{- 2}cm}{5.8 \times 10^{- 4}} = 14.5cm