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  4. A paper, with two marks having separation d, is held normal to the line of sight of an observer at distance of 50 m. The diameter of the eye lens of the observer is 2 mm. Light wavelength 5000 mathringA is made to fall on the lens. The least value of d, so that the marks can be seen as separate, will be :

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Q. A paper, with two marks having separation $d$, is held normal to the line of sight of an observer at distance of $50\, m$. The diameter of the eye lens of the observer is $2\, mm$. Light wavelength $5000\,\mathring{A}$ is made to fall on the lens. The least value of $d$, so that the marks can be seen as separate, will be :

AFMCAFMC 2002

Solution:

Resolving power is the ability of lens to measure the angular separation of images that are close together.
The resolving power of a lens is limited by diffraction effects. The lens aperture is a hole that is analogous to a two dimensional version of the single slit experiment.
For an ideal lens the resolution is
$d =\frac{1.22 \lambda \times D}{a}$
$d =\frac{1.22 \times 5000 \times 10^{-10} \times 50}{2 \times 10^{-3}}$
$=1.525\, cm$