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Q.

The headlights of a truck are 1.5 m apart. How far away could the truck and the headlights just be resolved by a person’s eye. (Take wavelength of light is 550 nm, diameter of pupil is 7 mm and refractive index of vitreous humor in eye is 1.36)

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a

10 km

b

21.28 km

c

20 km

d

None of these

answer is B.

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Detailed Solution

Let D=diameter of the eye lens, d=distance between the two sources ,  μ = refractive index of vitreous humor in eye  and distance of the truck=x  Resolving Power of the eye, 1θ= Dμ1.22λ but  tanθ=θ=dx ∴1θ= xd  ⇒xd= Dμ1.22λ ⇒x=Dμd1.22λ = 1.5×7×10−3×1.361.22×550×10−9=21.28×103m=21.28 km
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The headlights of a truck are 1.5 m apart. How far away could the truck and the headlights just be resolved by a person’s eye. (Take wavelength of light is 550 nm, diameter of pupil is 7 mm and refractive index of vitreous humor in eye is 1.36)