Physics - Wave Optics Question with Solution | TestHub

Given:
Radius of pupil, $r=0.25\text{ cm}=2.5\times 10^{-3}\text{ m}$
Diameter of pupil, $D=2r=5\times 10^{-3}\text{ m}$
Wavelength, $\lambda =500\text{ nm}=5\times 10^{-7}\text{ m}$
Viewing distance, $L=25\text{ cm}=0.25\text{ m}$

The angular resolution of the human eye is given by Rayleigh's criterion:
$\Delta \theta =\frac{1.22\lambda }{D}$

The minimum separation between two objects is:
$y=L\Delta \theta =\frac{1.22\lambda L}{D}$

Substituting the values:
$y=\frac{1.22\times 5\times 10^{-7}\times 0.25}{5\times 10^{-3}}$

$y=1.22\times 0.25\times 10^{-4}\text{ m}$

$y=0.305\times 10^{-4}\text{ m}$

$y=30.5\times 10^{-6}\text{ m}=30.5\mu \text{m}$

This is nearly $30\mu \text{m}$.

Answer: $30\mu \mathrm{m}$