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) 30μm b) 3μm c) 300μm d) 100 μm

Option a) 30μm.

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Diameter d=2r=2*0.25 = 0.5 cm.
the wavelength of light is λ=500nm=\(5*10^{-7}m\)\(sin\Theta =\frac{122\lambda }{d}\)\(sin\Theta =\frac{1.22*5*10^{-7}}{0.5*10^{-2}}\)\(sin\Theta =1.22*10^{-4}\)D=25 cm
Consider x as the minimum separation between two objects that the human eye can resolve.
\(sin\Theta =\frac{x}{D}\)\(x=Dsin\Theta\)\(x=0.25*1.22*10^{-4} = 30\mu m\)

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