Answer:
1) λ = 467.3 10⁻⁹ m = 467.3 nm
2) Δy = 2.9 10⁻³ m
Explanation:
1) The interference experiment is described by the expression
.d sin θ = m λ
It indicates that the wavelength is λ= 701 mn = 701 10⁻⁹ m and we have a first-order interference whereby m = 1, let's find the angle for which it occurs
d sin θ = m λ
d sin σ = λ₁ (1)
We are asked to find the wavelength so that destructive interference occurs at this same point, which is described by
d sin θ = (m + ½) λ (2)
In this case also m = 1
We substitute 1 in 2
λ₁ = (1 + ½) λ
λ = λ₁ /1.5
Let's calculate
λ = 701 10⁻⁹ /1.5
λ = 467.3 10⁻⁹ m = 467.3 nm
2) In this new experiment we must find the distance to each strip
Let's use trigonometry
tan θ = y / x
Furthermore, the angles in these experiments are very small, so we can approximate the tangent to the sine
tan θ = sin θ / cos θ = sin θ = y / x
We substitute
d y / x = m λ
In this case m = 2
y₁ = m λ x / d
y₁ = 2 692 10⁻⁹ 2 / 0.1 10⁻³
y₁ = 2.768 10⁻² m
For the other wavelength the interference is the third order m = 3
y₂ = 3 413 10⁻⁹ 2 / 0.1 10⁻³
y₂ = 2.478 10⁻² m
The distance between these two stripes is
Δy = y₁ - y₂
Δy = (2,768 - 2,478) 10⁻²
Δy = 2.9 10⁻³ m
