1. Tardigrade
  2. Question
  3. Physics
  4. The human eye has an approximate angular resolution of φ=6× 10- 4rad and a printer prints a minimum of 100dpi (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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Q. The human eye has an approximate angular resolution of $\phi=6\times 10^{- 4}rad$ and a printer prints a minimum of $100dpi$ (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?

NTA AbhyasNTA Abhyas 2020

Solution:

The linear distance between two dots is $\ell =\frac{2 . 54}{100}cm\sim eq2.54\times 10^{- 2}cm$ .
At a distance of $Zcm$ this subtends an angle $\phi\sim \ell /z\therefore z=\frac{1}{\phi}=\frac{2 . 54 \times 10^{- 2} cm}{6 \times 10^{- 4}}\approx45cm$ .