The smaller the angle to the 1st dark fringe the greater the resolution. If we suppose that the pupil is a circular opening of diameter $D$ we can write for this angle

$$
sintheta = 1.22frac{lambda}{d}.
$$
We see that the greater the wavelength the bigger the sine on the angle (which here means that the angle is also bigger since it falls in range of $0-90^circ$). This means that the resolution is greater with blue light since it has smaller wavelength and thus deviates at smaller angle.

Using the equation for the condition for 1st dark fringe we get

$$
sintheta=1.22frac{lambda}{D}.
$$
This yields for diameter of the aperture

$$
D=frac{1.22lambda}{sintheta} = frac{1.22times550times10^{-9}text{ m}}{sin0.000018^circ} =3.73text{ cm}.
$$