Ncert Exercises & Solutions

The human eye has an approximate angular resolution of $ϕ = 5.8 \times 10^{- 4}$ rad and a 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.

Hint: The distance z depends on the resolution of the human eye.

Step 1: Find the distance between two dots.

Given, the angular resolution of the human eye $ϕ = 5.8 \times 10^{- 4}$ rad.

and the printer prints 300 dots per inch.
The linear distance between two dots is, I= $\frac{2.54}{300} c m = 0.84 \times 10^{- 2} c m .$

Step 2: Use the formula of resolution.

At a distance of z cm, this subtends an angle, $ϕ = \frac{l}{z}$

$z = \frac{l}{ϕ} = \frac{0.84 \times 10^{- 2} c m}{5.8 \times 10^{- 4}} = 14.5 c m$

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