Answer:
Δy = 6.05 mm
Step-by-step explanation:
The double slit phenomenon is described by the expression
d sin θ = m λ constructive interference
d sin θ = (m + ½) λ destructive interference
m = 0,±1, ±2, ...
As they tell us that they measure the dark stripes, we are in a case of destructive interference, let's use trigonometry to find the sins tea
tan θ = y / x
y = x tan θ
In the interference experiments the measured angle is very small so we can approximate the tangent
tan θ = sin θ / cos θ
cos θ = 1
tan θ = sin θ
y = x sin θ
We substitute in the destructive interference equation
d (y / x) = (m + ½) λ
y = (m + ½) λ x / d
The first dark strip occurs for m = 0 and the third dark strip for m = 2. Let's find the distance for these and subtract it
m = 0
y₀ = (0+ ½) 480 10⁻⁹ 1.7 / 0.27 10⁻³
y₀ = 1.511 10⁻³ m
m = 2
y₂ = (2 + ½) 480 10⁻⁹ 1.7 / 0.27 10⁻³
y₂ = 7.556 10⁻³ m
The separation between these strips is Δy
Δy = y₂-y₀
Δy = (7.556 - 1.511) 10⁻³
Δy = 6.045 10⁻³ m
Δy = 6.05 mm