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A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate? The mean wavelength of visible light may be taken as 5000 Å (a) 1.25 m (b) 12.5 cm (c) 1.25 cm (d) 2.5 mm



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


        (a)    1.25 m


        (b)    12.5 cm


        (c)    1.25 cm


(d)    2.5 mm


Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago

(b)

Angular limit of resolution of eye, q =  where, d is diameter of eye lens.

Also, if y is the minimum separation between two objects at distance D from eye then

 

            

 

  Here, wavelength A = 5000 Å = 5 × 10-7 m

D = 50 m

        Diameter of eye lens = 2mm = 2 × 10-3

From eq. (1) minimum separation is

 

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