Respuesta :
Answer:
x = 2.6 10⁹ m
Explanation:
In order to differentiate the two stars, you must apply the Rayleigh criterion, which establishes that the objects are separated if the maximum diffraction of one coincides with the first minute of diffraction of the other.
Based on this, the diffraction for slits with m = 1
sin θ = λ / a
as the angles are very small
sin θ = θ
θ = λ / a
if instead of slits we use circular openings, the problem must be solved in polar coordinates, giving
θ = 1.22 λ /D
let's calculate
θ = 1.22 400 10⁻⁹ / 7.4
θ = 6.59 10⁻⁸ rad
this is the tiny angle to be able to see the stars separately, if we use the definition of radians
θ = x / R
where R is the distance to the system
x = θ R
let's reduce the distance to the SI system
R = 4.1 light-years (9.461 10¹⁵ m / 1 light-year)
R = 3.88 10¹⁶ m
let's calculate
x = 6.59 10⁻⁸ 3.88 10¹⁶
x = 2.6 10⁹ m
this is the minimum distance between the two stars to be able to differentiate them
The minimum distance between the two stars is mathematically given as
x=2.6e9m
Distance between the two stars
Question Parameters:
If the star system is 4.1 light-years away and she is observing with blue light (400 nm) using a telescope with a 7.4 meter circular primary mirror,
Generally the equation for the diffraction for slits is mathematically given as
sin θ = λ / a
Therefore
\theta = 1.22 λ /D
\theta= 6.59 10⁻⁸ rad
Therefore, the minimum distance between the two stars is
x= 6.59e-8 * 3.88e16
x=2.6e9m
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