Answer:
λ = 6.802 10⁻⁷ m, wavelength corresponds to orange almost red
Explanation:
The expression for constructive interference is
d sin θ = m λ
let's use trigonometry
tan θ = y / L
tan θ = sin θ / cos θ
interference experiments angles are very small
tan θ = sin θ = y / L
substituting
= m λ
in this case they indicate the separation of the slits d = 7.16 10-5 m, the order of the interference is m = 4, the distance y = 3.8 10-2 m and the separation to the screen L = 1 m
A) they ask us for the wavelength
λ =
let's calculate
λ = 7.16 10⁻⁵ 3.8 10⁻² /(4 1)
λ = 6.802 10⁻⁷ m
B) Let's reduce the wavelength to nm
λ = 6.802 10⁻⁷ m (109 nm / 1m)
λ = 680.2 nm
this wavelength corresponds to orange almost red