The limit to the eye’s visual acuity is related to diffraction by the pupil. randomized variables d = 3.05 mm dh = 1.05 m show answer no attempt 33% part (a) what is the angle between two just-resolvable points of light for a 3.05 mm diameter pupil in radians, assuming an average wavelength of 550 nm?

θ = 2 10⁻⁴ rad

Explanation:

The resolution of two nearby light sources is determined by the diffraction phenomenon and several criteria have been established, one of the most used is the Rayleigh criterion, that the image is resolved when the maximum of a diffraction pattern coincides with the first minimum of the other diffraction pattern

The equation that describes diffraction is

     a sin θ = m λ        m = ±1, ±2, ...

According to Rayleigh's criteria the first minimum occurs for m = 1, in addition to the diffraction measures the angles are very small, so we approximate the sin θ≅ θ

      θ = lam / a

This expression linear slits, in the case of circular openings, we must use polar coordinates for the resolution of the system, in these coordinates a numerical factor is introduced and the equation is

     θ = 1.22 λ / D

D is the diameter of the circular opening

Let's apply this last equation to our case.

     θ = 1.22  550 10⁻⁹ / 3.05 10⁻³

     θ = 220 10⁻⁶ rad

     θ = 2 10⁻⁴ rad