Step 1: Understanding the Uniaxial Negative Optic Sign.
In mineralogy, the optic sign of a uniaxial mineral refers to how the refractive indices for light traveling in different directions are related. For a uniaxial negative mineral, the refractive index of the extraordinary ray (\(n_e\)) is less than the refractive index of the ordinary ray (\(n_o\)).
Step 2: Analyzing the Options.
- Option (A): The ordinary ray is slow, but this is not a specific indicator of the optic sign.
- Option (B): The extraordinary ray being slow is a feature of uniaxial positive minerals, not negative.
- Option (C): The condition \(n_e<n_o\) is the defining characteristic of uniaxial negative minerals.
- Option (D): \(n_e>n_o\) is the condition for uniaxial positive minerals.
Thus, the correct answer is (C) \(n_e<n_o\).
Final Answer:
\[
\boxed{n_e<n_o}
\]