First slide

Resolving power of optical instruments

Question

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)

Moderate

A

10 km
B

21.28 km
C

20 km
D

None of these

Solution

$L e t D = d i a m e t e r o f t h e e y e l e n s, d = d i s \tan c e b e t w e e n t h e t w o s o u r c e s, μ = r e f r a c t i v e i n d e x o f v i t r e o u s h u m o r i n e y e a n d d i s \tan c e o f t h e t r u c k = x R e s o l v i n g P o w e r o f t h e e y e, \frac{1}{θ} = \frac{D μ}{1.22 λ} b u t \tan θ = θ = \frac{d}{x} ∴ \frac{1}{θ} = \frac{x}{d} \Rightarrow \frac{x}{d} = \frac{D μ}{1.22 λ} \Rightarrow x = \frac{D μ d}{1.22 λ} = \frac{1.5 \times 7 \times 10^{- 3} \times 1.36}{1.22 \times 550 \times 10^{- 9}} = 21.28 \times 10^{3} m = 21.28 k m$

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