At what distance could one theoretically distinguish two automobile headlights separated by 1.5 meters? ?

Assume a pupil diameter of 0.50 cm and yellow headlights seen at the wavelength 5.0 x 10^-7 m. Assume eye fluid has an average n = 1.33.

a. 6.0 km 

b. 12 km 

c. 9.0 km 

d. 3.0 km 

e. 16 km 

Ans: ethx

Update:

@NCS

Thank you for answering!

I wonder why you use r = d / φ to calculate the final answer.

3 Answers

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  • NCS
    Lv 7
    1 month ago
    Favorite Answer

    a*sinΘ = 1.22λ → → a the aperture diameter

    0.50e-2m * sinΘ = 1.22*5.0e-7m → → sinΘ = 1.22e-4

    φ = arcsin[sinΘ / n] = arcsin[1.22e-4 / 1.33] = 9.17e-5 rads

    r = d / φ = 1.5m / 9.17e-5rads = 16352 m ≈ 16 km ◄

    Source(s): d = rΘ ------ subtended arc = radius * subtended angle
  • 1 month ago

    @NCS

    Thank you for answering!

    I wonder why you use r = d / φ to calculate the final answer.

  • 1 month ago

    I will guess that at a distance of 10 meters, one could easily theoretically distinguish two headlights that are separated by 1.5 meters. It would be a cinch to distinguish these headlights at that distance. 

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