Two point white dots are 1, mm apart on a bla | vedclass

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(B) The condition for the resolution of two point objects is given by the Rayleigh criterion: $	heta \geq 1.22 \frac{\lambda}{d}$,where $	heta = \fr

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$5$

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(B) The condition for the resolution of two point objects is given by the Rayleigh criterion: $	heta \geq 1.22 \frac{\lambda}{d}$,where $	heta = \frac{y}{D}$.Here,$y = 1\, mm = 10^{-3}\, m$ is the separation between the dots,$d = 3\, mm = 3 	imes 10^{-3}\, m$ is the diameter of the pupil,and $\lambda = 500\, nm = 5 	imes 10^{-7}\, m$ is the wavelength of light.Substituting these values into the inequality $\frac{y}{D} \geq 1.22 \frac{\lambda}{d}$,we get:$D \leq \frac{y d}{1.22 \lambda} = \frac{10^{-3} 	imes 3 	imes 10^{-3}}{1.22 	imes 5 	imes 10^{-7}}$$D \leq \frac{3 	imes 10^{-6}}{6.1 	imes 10^{-7}} = \frac{30}{6.1} \approx 4.918\, m$.Rounding to the nearest integer,the maximum distance is approximately $5\, m$.

Two point white dots are $1\, mm$ apart on a black paper. They are viewed by an eye with a pupil diameter of $3\, mm$. Approximately,what is the maximum distance in $m$ at which these dots can be resolved by the eye? [Take wavelength of light $\lambda = 500\, nm$]

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