A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of $$50m$$. The diameter of the $$eye-lens$$ of the observer is $$2mm$$. Find the least value of d (in$$ $$cm), so that the marks can be seen as separate? The mean wavelength of visible light may be taken as $$5000$$ $$A0$$

Question

A  paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of $$50m$$. The diameter of the $$eye-lens$$ of the observer is $$2mm$$. Find the least value of d (in$$ $$cm), so that the marks can be seen as separate? The mean wavelength of visible light may be taken as $$5000$$ $$A0$$

Infinity Learn · Accepted Answer

Angular limit of resolution of eye, θ$$=$$λd ,  where, d is diameter of eye lens.  Also, if y is the minimum separation between two objects at distance D from eye then θ$$=yD$$ ⇒$$yD=$$λd ⇒$$y=$$λDd.........................$$.1$$ Here, wavelength λ$$=5000A0=5$$×$$10$$−$$7m$$  $$D=50$$ m  Diameter of eye lens  $$=$$ $$2$$ mm $$=$$ $$2$$×$$10$$−$$3m$$  From eq.(1) minimum separation is  $$y=5$$×$$10$$−$$7$$×$$502$$×$$10$$−$$3=12.5$$×$$10$$−$$3m=1.25$$ cm

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