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(B) According to the Rayleigh criterion for a circular aperture,the angular resolution $	heta$ is given by $	heta = 1.22 \lambda / D$,where $\lambda

Vedclass · Accepted Answer

$30$

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(B) According to the Rayleigh criterion for a circular aperture,the angular resolution $	heta$ is given by $	heta = 1.22 \lambda / D$,where $\lambda$ is the wavelength and $D$ is the diameter of the aperture.Given: Wavelength $\lambda = 500 \ nm = 500 	imes 10^{-9} \ m$,Radius $r = 0.25 \ cm = 2.5 	imes 10^{-3} \ m$,so Diameter $D = 2r = 5.0 	imes 10^{-3} \ m$.The angular resolution is $	heta = (1.22 	imes 500 	imes 10^{-9}) / (5.0 	imes 10^{-3}) = 1.22 	imes 10^{-4} \ rad$.The minimum separation $d$ at a distance $L = 25 \ cm = 0.25 \ m$ is $d = L 	imes 	heta$.$d = 0.25 	imes 1.22 	imes 10^{-4} = 0.305 	imes 10^{-4} \ m = 30.5 	imes 10^{-6} \ m = 30.5 \mu m$.Thus,the minimum separation is nearly $30 \mu m$.

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

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