Yes, because if you exceed the critical angle you will be out of the acceptance angle and the light will not reflect properly and the resulting signal will not be usable.

as we know that we apply light ray as source instead of electricity in case of OFC (optical fiber cable) communication but not all ray will propagate so that only those rays that have an angle greater than the critical angle can be transmitted and that reference angle is called ACCEPTANCE ANGLE.

maximam angle through which light can b injected to a optical fiber for its total intenal reflection

When talking about numerical aperture it is mainly used in microscopy, which helps describe the acceptance area angle of an objective. The numerical aperture can found using this formula NA=nx

Acceptance is...