Answer:
= 4,574 10⁻⁵ m
Explanation:
The interference pattern for a two slit system is given by
d sin θ = m λ constructive interference
d sin θ= (m + ½) λ destructive interference
In general and also in this case the screen is far from the slits, so the TT-free can approach the TT
tan θ = y / L
Let's replace
d y / L = m λ constructive interference
d y / L = (m + ½) λ destructive interference
Let's start when there is constructive interference
They give us the frequency of light, let's find the wavelength
c = λ f
λ = c / f
λ = 3 10⁸ / 6.32 10¹⁴
λ = 4.7468 10⁻⁷ m
Let's take the opportunity to reduce the SI system
L = 87 cm = 0.87 m
y = 3.16 cm = 0.0316 m
Now we can find the separation of the slits
d = m λ L / Y
d = 3 4.7468 10⁻⁷ 0.87 / 0.0316
d = 3.92 10⁻⁵ m
We already have all the data, now let's use the destructive interference equation and find
d / L = (m + ½) λ
= (m + ½) λ L / d
= (3 + ½) 4.7468 10⁻⁷ 0.87 / 0.0316
= 4,574 10⁻⁵ m