Respuesta :
Answer:
The most correct option is;
B. 10 km
Explanation:
[tex]L = \frac{y \times d}{1.22 \times \lambda} = \frac{1.2 \times 0.004}{1.22 \times 400 \times 10^{-9}} = 9836.066 \ km[/tex]
Where:
y = Distance between the two headlights
d = Aperture of observers eye
λ = Wavelength of light
L = Distance between the observer and the headlight
Therefore, from the above solution, the distance between the observer and the headlights is 9386.066 km which is approximately 10 km.
Also we have
sinθ = y/L = 1.22 (λ/d)
[tex]= 1.22 \times \frac{400 \times 10^{-9}}{0.004}[/tex]
sinθ = 1.22×10⁻⁴ rad
Answer:
L = 9836.1 m ≈ 10 km
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
