Answer:
θ₁ = 3.35 10⁻⁴ rad , θ₂ = 8.39 10⁻⁵ rad
Step-by-step explanation:
This is a diffraction problem for a slit that is described by the expression
sin θ = m λ
the resolution is obtained from the angle between the central maximum and the first minimum corresponding to m = 1
sin θ = λ / a
as in these experiments the angle is very small we can approximate the sine to its angle
θ = λ / a
In this case, the circular openings are explicit, so the system must be solved in polar coordinates, which introduces a numerical constant.
θ = 1.22 λ / D
where D is the diameter of the opening
let's apply this expression to our case
indicates that the wavelength is λ = 550 nm = 550 10⁻⁹ m
the case of a lot of light D = 2 mm = 2 10⁻³ m
θ₁ = 1.22 550 10-9 / 2 10⁻³
θ₁ = 3.35 10⁻⁴ rad
For the low light case D = 8 mm = 8 10⁻³
θ₂ = 1.22 550 10-9 / 8 10⁻³
θ₂ = 8.39 10⁻⁵ rad