Question

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

• A. $300 \, μm$
• B. $1 \, μm$
• C. $30 \, μm$
• D. $100 \, μm$

Answer 1

Answer: (C)

By Fraunhofer diffraction through a circular aperture, $\theta =\frac{1 .22 \lambda }{d}$

$d=$ diameter of pupil $=2\times \text{0.25}=\text{0.5} \, cm$
$\lambda =500 \, nm$ . 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 $ $=\frac{25 \times 10^{- 2} \times 1.22 \times 500 \times 10^{- 9}}{5 \times 10^{- 3}}m$
$D\theta =30\times 10^{- 6}m$ $\Rightarrow D\theta =30 \, μm$ .