Answer
Yes, one can resolve those 2 stars with the naked eye.
Work Step by Step
Find the angular separation of Mizar and Alcor.
$$(12\;arc\;min)(\frac{0.016667 deg}{1\;arc\;min })(\frac{\pi\;rad}{180\;deg})=3.49\times10^{-3}rad$$
Using numbers from Example 25-11, assume that the pupil is 3.0 mm in diameter and that light’s wavelength is 550 nm.
Calculate the minimum angular separation that the human eye could resolve, following Example 25-10.
$$\theta=\frac{1.22\lambda}{D}=\frac{1.22(550\times10^{-9}m)}{0.003m}=2.24\times10^{-4}rad$$
This angle is considerably smaller than the angular separation of Mizar and Alcor. The stars are resolvable by the naked eye.
