Two luminous point sources separated by a certain distance are at 10 ~km from an observer. If the aperture of his eye is 2.5 10⁻³ ~m and the wavelength of light used is 500 ~nm , the distance of separation between the point sources just seen to be resolved is

Step-by-step solution

According to Rayleigh's criterion, = 1.22 d _ e where = wavelength of light, d _ e = diameter of the pupil of the eye = 1.22 500 10⁻⁹ 2.5 10⁻³ =2.44 10⁻⁴ radian But = a D Distance of separation, aligned a = D &=10 10³ 2.44 10⁻⁴ &=2.44 ~m aligned