Two candles are lit and separated by 0.10 m. If the diameter of the pupil of an observer's eye is 3.5 mm, what is the maximum distance that the candles can be away from the observer and be seen as two light sources? Use 545 nm for the wavelength of light in the eye.
A)170 m
B)340 m
C)530 m
D)680 m
E)850 m

Question

Quizplus · Accepted Answer

According to Rayleigh's criterion, two light sources can be distinguished if the central maximum of one source falls on the first minimum of the other. This occurs when the angle between the two sources is:
sin θ = 1.22 λ/D
where λ is the wavelength of the light, D is the diameter of the pupil, and θ is the angular separation between the two sources.

Rearranging this formula, we get:
D = 1.22 λ/sin θ

For the given problem, θ = tan-1(0.05/0.10) = 26.57° (the distance between the candles is equal to the tangent of the angular separation angle)
Plugging in the values, we get:
D = 1.22 x 545 x 10^-9 / sin 26.57°
D ≈ 3.4 x 10^-6 m

Therefore, for the observer to distinguish the two light sources, the maximum distance between the candles can be:
distance = D / tan θ
distance = (3.4 x 10^-6) / tan 26.57°
distance ≈ 528 m

Thus, the best choice is (C) 530 m.

Two Candles Are Lit and Separated by 0