Question

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

$x=Dsin\theta =.25\times 1.22\times {10}^{-4}=30\times {10}^{-6}=30\mu m$