Question

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

• A. 20.32 cm
• B. 29.50 cm
• C. 14.59 cm
• D. 6.85 cm

Answer 1

The Correct Option is C

Given:
Angular resolution of human eye: \( \theta = 5.8 \times 10^{-4} \) rad
Print resolution: 300 dpi = 300 dots per inch
1 inch = 2.54 cm

Step 1: Convert dpi to dot size
Dots per cm = \( \frac{300}{2.54} \approx 118.11 \) dots/cm
So, distance between two dots (linear resolution) is:
\[ s = \frac{1}{118.11} \approx 8.47 \times 10^{-3} \text{ cm} \] 

Step 2: Use small angle approximation
\[ \theta \approx \frac{s}{d} \Rightarrow d \approx \frac{s}{\theta} = \frac{8.47 \times 10^{-3}}{5.8 \times 10^{-4}} \approx 14.59 \text{ cm} \] 

Answer: 14.59 cm