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The maximum incident angle that results in total internal reflection in fiber optics is defined by the critical angle. This critical angle is determined by the refractive indices of the two media at the interface; specifically, it is the angle of incidence beyond which light will not pass into the second medium but instead will be reflected entirely within the first medium.

When light travels from a medium with a higher refractive index to a medium with a lower refractive index, total internal reflection occurs if the angle of incidence is greater than the critical angle. This property is essential in fiber optics, as it enables the efficient transmission of light signals along the fiber by ensuring that the light remains confined within the core of the fiber, allowing it to travel long distances with minimal loss.

The other options pertain to different concepts within optics. The refractive gradient is related to a change in refractive index within a material rather than the specific angle for total internal reflection. The transmission angle does not have a defined role in the context of total internal reflection. Lastly, the attenuation rate refers to the reduction in power of the transmitted signal over distance, which does not direct relate to the angles involved in the reflection process.