Answer:
L = 9836.1 m ≈ 10 km
Step-by-step explanation:
Given:-
- The separation between head-lights, s = 1.2 m
- The wavelength of light emitted, λ = 400 nm
- The aperture of an eye, d = 4.0 mm
Find:-
What is the distance between the observer and the headlights?
Solution:-
- We will assume the observer is located in between two headlights and the distance between the observer an each headlight is same and equal to (L).
- We will apply the results of Young's split ( interference experiment ). Where the angle of separation between interference pattern form ( θ ). Also the angle of separation between observer and head light. is related to the wavelength and slit opening.
sin ( θ ) = 1.22*λ / d
- Determine the angle of separation θ :
θ = arc sin ( 1.22*(00*10^-9 / 0.004) )
θ = arc sin (0.000122)
θ = 0.000122 rads
- Using trigonometric ratios we can determine the distance between the headlights and the observer:
sin ( θ ) = s / L
sin ( 0.000122 ) = s / L
0.000122 = 1.2 / L
L = 1.2 / 0.000122
L = 9836.1 m ≈ 10 km