The correct answer is $\boxed{\text{C}}$.
The smallest depth that can be discerned by the human eye is given by the formula:
$$d = \frac{2 \tan \theta}{f}$$
where $d$ is the depth, $\theta$ is the smallest measurable angle, and $f$ is the focal length of the eye.
The smallest measurable angle is 20 arcminutes, which is equal to $\frac{1}{3600} \pi$ radians. The focal length of the eye is approximately 6.5 cm.
Substituting these values into the formula, we get:
$$d = \frac{2 \tan \left( \frac{1}{3600} \pi \right)}{0.065} = 1.00 \text{ mm}$$
Therefore, the smallest depth that can be discerned by the human eye is 1.00 mm.
Option A is incorrect because it is half the correct value. Option B is incorrect because it is twice the correct value. Option D is incorrect because it is greater than the correct value.