Question 151 of 191

Assuming that the human pupil has a radius of $0.25cm$ and a comfortable viewing distance of $25cm$. The minimum separation between two point objects that the human eye can resolve for the light of wavelength $500nm$ is

A$300\mu m$B$1\mu m$C$30\mu m$D$100\mu m$

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Answer: (C) $30\mu m$

By Fraunhofer diffraction through a circular aperture, $\theta =\dfrac{1.22\lambda }{d}$

$d=$ diameter of pupil $=2\times \text{0.25}=\text{0.5}cm$
$\lambda =500nm$. The first dark ring is formed by the light diffracted from the hole at an angle $\theta$ with the axis. Viewing distance, $D=25cm$$∴$ The minimum separation between $2$ objects $=D\theta$$=\dfrac{25\times {10}^{-2}\times 1.22\times 500\times {10}^{-9}}{5\times {10}^{-3}}m$
$D\theta =30\times {10}^{-6}m$$\Rightarrow D\theta =30\mu m$.