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Oct 3, 2017

The Rayleigh criterion for diffraction-limited vision for the minimum resolvable detail of objects located at a distance #D#, using a circular aperture (an iris) of diameter of #d_e# and light of wavelength #lambda# is given by the expression

#sintheta_D=1.22lambda/theta_D#

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Inserting given values we get
#sintheta=1.22xx(500xx10^-9)/(2.5xx10^-3)=2.44xx10^-4#

We know that for very small value of #sin theta#

#sintheta~~theta#
#=>theta~~2.44xx10^-4" radian"#

#a# is the distance of separation of the objects being resolved. From the figure, for small angles

#a=thetaxxD#

Inserting calculated and given values we get

#a=(2.44xx10^-4)xx(10xx10^3)=2.44" m"#

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