JEE Main · 2015 · 04 Apr 2015 · Offline · Wave Optics

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Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm , the minimum separation between two objects that human eye can resolve at 500 nm wavelength is:

(A) $30 μ m$ ✓ Correct
(B) $100 μ m$
(C) $300 μ m$
(D) $1 μ m$

Answer: (A)

Solution

Diffraction at the pupil sets the finest detail the eye can split, through the Rayleigh criterion

θ = 1.22 \frac{λ}{D}

. The pupil diameter is

D = 2 \times 0.25

= 0.5

cm, so with

λ = 500

nm,

θ = 1.22 \times \frac{500 \times 1 0 ^{- 9}}{0.5 \times 1 0 ^{- 2}} \approx 1.22 \times 1 0^{- 4}

rad. At the viewing distance

d = 25

cm the two objects must be at least

s = d θ = 0.25 \times 1.22 \times 1 0^{- 4} \approx 3 \times 1 0^{- 5}

m apart, i.e. about

30 μ

JEE Main · 2015 · 04 Apr 2015 · Offline · Single correct option

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