Answer:
Λ = 5.14 10⁻⁴ m
Explanation:
This is a double slit experiment, which for the case of constructive interference
d sin θ = m λ
let's use trigonometry
tan θ = y / L
as the angles are very small
tan θ = [tex]\frac{sin \theta}{cos \theta}[/tex] = sin θ
sin θ = y / L
we substitute
d y / L = m λ
y = m λ L / d
we calculate for the interference of order m = 5
y = 5 527 10⁻⁹ 1.54/0.102 10⁻³
y = 3.978 10⁻² m
Now we can find the difference in length between the two rays, that of the central maximum and this
let's use the Pythagorean theorem
L’= [tex]\sqrt{L^2 +y^2}[/tex]
L ’= [tex]\sqrt{1.54^2 +(3.978 \ 10^{-2})^2 }[/tex]
L ’= 1.54051 m
optical path difference
Λ = L’- L
Λ = 1.54051 - 1.54
Λ = 5.14 10⁻⁴ m
