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?

Question

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? (A) 30cm (B) 45cm (C) 100cm (D) 200cm

Tardigrade Admin · Accepted Answer

The linear distance between two dots is ℓ =(2 . 54/100)cm∼ eq2.54× 10- 2cm . At a distance of Zcm this subtends an angle φ∼ ℓ /z∴ z=(1/φ)=(2 . 54 × 10- 2 cm/6 × 10- 4)≈45cm .

Q. The human eye has an approximate angular resolution of $ϕ = 6 \times 1 0^{- 4} r a d$ and a printer prints a minimum of $100 d p i$ (dots per inch, $1 in c h = 2.54 c m$ ). At what minimal distance $z$ should a printed page be held so that one does not see the individual dots?

$30 c m$

$45 c m$

$100 c m$

$200 c m$

The linear distance between two dots is $ℓ = \frac{2.54}{100} c m \sim e q 2.54 \times 1 0^{- 2} c m$ .
At a distance of $Z c m$ this subtends an angle $ϕ \sim ℓ / z ∴ z = \frac{1}{ϕ} = \frac{2.54 \times 1 0 ^{- 2} c m}{6 \times 1 0 ^{- 4}} \approx 45 c m$ .

Q. 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?

30cm

45cm

100cm

200cm