Acceptance angle in fiber optics is defined purely based on ray optics (geometrical aspect). According to the Ray Model of Light, the angle of incidence of a ray determines whether or not it will be coupled into the fiber core and allowed to transit through it via total internal reflection. 

The maximum incidence angle of an optical fiber at which the light can enter the core is known as the acceptance angle. So, any ray with an incident angle less than the acceptance angle can be guided through the fiber.

Acceptance angle is related to the numerical aperture of an optical fiber.

Numerical Aperture is a dimensionless quantity that determines the ability of a system to gather light. It is the measure of the range of angles over which the system can accept light or the angular acceptance of a system for the incoming light.

Here n is the refractive index of the medium from which light is entering the fiber and θ is the acceptance angle.

We have another equation for the numerical aperture as,

Where n₁ is the refractive index of the core and n₂ is the refractive index of the cladding.

From the above equation, the acceptance angle can be calculated as,