JEE Main · 2005 · 08 May 2005 · Offline · Wave Optics

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Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light

= 500

nm]

(A)5 m✓ Correct
(B)1 m
(C)6 m
(D)3 m

Answer: (A)

Solution

By Rayleigh's criterion the eye just resolves an angular separation

θ = \frac{1.22 λ}{D}

with pupil

D = 3

mm. The two dots

d = 1

mm apart subtend

θ = \frac{d}{R}

at distance

R

. Equating,

R = \frac{d D}{1.22 λ} = \frac{( 1 0 ^{- 3} ) ( 3 \times 1 0 ^{- 3} )}{1.22 \times 500 \times 1 0 ^{- 9}} \approx 5

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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