Question

A paper, with two marks having separation $d$, is held normal to the line of sight of an observer at distance of $50m$. The diameter of the eye lens of the observer is $2mm$. 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 :

• A. 2.125 cm
• B. 1.525 cm
• C. 0.125 cm
• D. 1.225 cm

Answer 1

Answer: (B)

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
$d=\frac{1.22\lambda \times D}{a}$
$d=\frac{1.22\times 5000\times 10^{-10}\times 50}{2\times 10^{-3}}$
$=1.525cm$