Question

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. $100\mu m$

Answer 1

Answer: (C)

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

$d=$ 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, $D=25cm$ $\therefore$ The minimum separation between $2$ objects $=D\theta$ $=\frac{25\times 10^{-2}\times 1.22\times 500\times 10^{-9}}{5\times 10^{-3}}m$
$D\theta =30\times 10^{-6}m$ $\Rightarrow D\theta =30\mu m$ .