Question

Question #6f7cd

Answer 1

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`

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"`