Answer:
a) d = 3.76 10⁻⁵ m , b) y = 3.61 10⁻² m
Explanation:
The interference phenomenon is described by the expression
d sin θ = m λ
Where d is the separation of the slits, λ the wavelength and m an integer indicating the interference number
Let's apply to this case, as we observe the third order m = 3
a) Let's use trigonometry to find the angles
tan θ = y / x
The phenomena of interference and diffraction angles are very small, so
tan θ = sin θ / cos θ = sin θ
sin θ = y / x
We replace
d y / x = m λ
d = m λ x / y
The frequency of the light is
c = λ f
λ= c / f
Let's calculate
λ = 3 10⁸ / 6.34 10¹⁴
λ = 4.73 10⁻⁷ m
d = 3 4.73 10⁻⁷ 0.820 / 0.0309
d = 376.56 10⁻⁷ m
d = 3.76 10⁻⁵ m
b) for destructive interference we must add ½ Lam
d sin θ = (m + ½) λ
d y / x = (m + ½) λ
y = (m + ½) λ x / d
Let's calculate
y = (3+ ½) 4.73 10⁻⁷ 0.820 / 3.76 10⁻⁵
y = 3.61 10⁻² m
