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The approximate angular resolution for human eye is $ϕ = 5.08 \times 10^{- 4}$ rad and typical photo printer prints a minimum of 360 dpi (dots per inch , 1 inch =2.54 cm) when the printed page is held at a minimum distance of $α c m$ then one can not see the individual dots. Write the value of $[α],$ where [] is the greatest integer function

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answer is 13.

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Detailed Solution

The angular resolution of human eye, $ϕ = 5.08 \times 10^{- 4} r a d$ the linear distance between two successive dots in typical photo printer $l = \frac{2.54}{360} c m$ at distance of Z cm, the gap distance $l$ subtend an angle $ϕ = \frac{l}{Z}$

$∴ Z = 1.5 = \frac{2.54 \times 10^{- 2}}{360 \times 5.08 \times 10^{- 4}} = 13.89 c m = α$

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