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JEE Main 20154 April
Exam
JEE Main
Year
2015
Date
4 April
Subject
Physics
Chapter
Wave Optics

JEE Main 2015 · 4 April · Physics · Wave Optics

Assuming that the human pupil has a radius of 0 . 25cm and a...

Assuming that the human pupil has a radius of 0.25cm0 . 25cm and a comfortable viewing distance of 25cm25cm. The minimum separation between two point objects that the human eye can resolve for the light of wavelength 500nm500nm isAssuming that the human pupil has a radius of 0 . 25cm and a comfortable viewing distance of 25cm . The minimumAssuming that the human pupil has a radius of 0 . 25cm and a comfortable viewing distance of 25cm . The minimum

Options

  1. A300μm300\mu m
  2. B1μm1\mu m
  3. C30μm30\mu m
  4. D100μm100\mu m

Correct answer

C. 30μm30\mu m

Step-by-step solution

By Fraunhofer diffraction through a circular aperture,& θ=1.22λd\theta = \dfrac{1 .22 \lambda}{d}
Assuming that the human pupil has a radius of 0 . 25cm and a comfortable viewing distance of 25cm . The minimum
d=d = diameter of pupil~=2×0.25=0.5cm= 2 \times \text{0.25} = \text{0.5}cm
λ=500nm\lambda = 500nm. The first dark ring is formed by the light diffracted from the hole at an angle θ\theta with the axis. Viewing distance,~D=25cm∴D = 25cm∴~The minimum separation between 22 objects =Dθ=25×10−2×1.22×500×10−95×10−3m= D\theta= \dfrac{25 \times {10}^{- 2} \times 1.22 \times 500 \times {10}^{- 9}}{5 \times {10}^{- 3}}m
Dθ=30×10−6m⇒Dθ=30μmD\theta = 30 \times {10}^{- 6}m⇒ D\theta = 30\mu m.
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