Answer:
λ = 6,108 10⁻⁷ m = 610.8 nm
λ = 5.513 10⁻⁷ m = 551.3 nm
Explanation:
Young's double slit experiment results in a pattern consisting of maxima and minima of interference, the maximums are described by the expression
d sin θ = m λ
where d of the distance between the two slits, θ is the angle from the central maximum to the given interference line, λ the wavelength of the radiation and an integer indicating the order of interference
In this exercise they give us several conditions
The first
the angle is 1.12º to the maximum m = 8
the distance between the slits d = 0.000250 m
of the initial equation
λ = d sin θ / m
λ = 0.000250 sin 1.12 / 8
λ = 6,108 10⁻⁷ m = 610.8 nm
The second
the distance from the slits to the screen is L = 302.0 cm = 3.020 m
the distance from the central maximum is y = 3.33 cm = 0.0333 m for interference m = 5
in this case we use that the angle in the experiment is small
tan θ = y / L
tan θ = sin θ / cos θ = sin θ
we substitute
sin θ = y / L
d y / L = m λ
λ = d y / L m
we calculate
λ = 0.000250 0.0333 / (3,020 5)
λ = 5.513 10⁻⁷ m = 551.3 nm
