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

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