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
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)