Answer:
a)λ = 6.133 10⁻⁷ m
= 613.3 nm, b) d = 1.60 10⁻⁶ m
, c) Δd = 0.24 10⁻⁶ m
Explanation:
The expression that describes the interference phenomenon for the double slit is
d sin θ = m λ m = ±1, ±2,…
a) Let's use the data to find the separation of the slits (d)
d = m λ / sin θ
d = 4 460 10⁻⁹ / sin 90
d = 1.84 10⁻⁶ m
Now we can calculate the minimum wavelength for the third orcen (m = 3), the maximum angle must be 90 °
λ = d sin θ / m
λ = 1.84 10⁻⁶ sin 90 / 3
λ = 6.133 10⁻⁷ m
This is the last visible wavelength in this interference order, that is, we see the light with a shorter length than the calculated
b) To eliminate all the light of the fourth order (m = 4) let's use the minimum wavelength of visible range ( λ = 400 nm) from a 90 ° angle
d = m λ / sin θ
d = 4 400 10⁻⁹ / sin 90
d = 1.60 10⁻⁶ m
If we reduce the slit to this value, the spectrum for the fourth order can be used.
c) It is change of separation is
Δd = d₂ - d₁
Δd = (1.84 - 1.60) 10⁻⁶ m
Δd = 0.24 10⁻⁶ m
