Step 1: Understand the definition of paraxial rays.
Paraxial rays are light rays that travel very close to the principal axis of an optical system and make very small angles with it. By definition, the angle between paraxial rays and the principal axis is approximately \( 0^\circ \).
Step 2: Analyze the options.
Final Answer: The angle between the paraxial rays and the principal axis is \( \mathbf{0^\circ} \), which corresponds to option \( \mathbf{(2)} \).