Question

Assuming human pupil to have a radius of $0.25cm$ and a comfortable viewing distance of $25cm$, the minimum separation between two objects that the human eye can resolve at $500nm$ wavelength is

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

Answer 1

The correct option is B $30\mu m$

Diameter $d=2r=2\times 0.25=0.5cm$. The wavelength of light is $\lambda =500nm=5\times {10}^{-7}m$.

We have the formula $sin\theta =\frac{1.22\lambda }{d}$
or
$sin\theta =\frac{1.22\times 5\times {10}^{-7}}{0.5\times {10}^{-2}}=1.22\times {10}^{-4}$

Also $D=25cm$

Let $x$ be the minimum separation between two objects that the human
eye can resolve.

Thus $sin\theta =\frac{x}{D}$
or
$x=Dsin\theta =30\mu m$