Acceptance Angle and Numerical Aperture - Optical Fiber Communication - Optical Fibre - NA

This video describes, What is Acceptance Angle, Acceptance Cone with Diagram and also what is Numerical Aperture (NA), relation between numerical aperture and acceptance angle and various formulas to calculate Numerical Aperture.

Definition of Acceptance Angle
Acceptance angle is the maximum angle with the axis of the Optical Fiber at which the light can enter into the optical fiber in order to be propagated through it.

Structure and Working of the Optical Fiber
Now observe this diagram carefully, two layers of the Optical Fiber- Core and Cladding can be seen in the diagram. These are drawn in pink color. The light rays propagate inside the core that has another layer over it, known as cladding.

Although other protective layers are also there over the cladding layer, But only core and cladding are shown in this image, which is enough to clear the concepts.
The refractive index (the ratio of speed of light in vacuum and the speed of light in the medium) of the core is more than the refractive index of the cladding.
As we also know that, when a light ray propagates from a denser medium to the rarer medium, it deviates away from the normal. But when the angle of incidence is more than the critical angle then this light ray returns back into the same medium. This phenomena is called as the 'Total Internal Reflection' (TIR).
Although it is a special case of refraction where the incidence angle is more than the critical angle, but here it seems like a reflection phenomena and the light ray is totally reflected back into the same medium. Therefore this phenomena is known as the Total Internal Reflection (TIR).
The same phenomena of total internal reflection takes place in the optical fibre. Here the core acts as a denser medium while the cladding as a rarer medium. So the light rays propagate inside the core of the optical fiber with the total internal reflections.
But as we have already discussed that for the total internal reflection to take place, it is required that the incidence angle must be more than the critical angle. If this condition is satisfied then the light ray can propagate inside the core of The optical fiber with total internal reflection.
Now again observe the image. This image shows two light rays. Focus on any one light ray. You will see that total internal reflection takes place inside the core every time at the core cladding interface. The reflected ray after total internal reflection acts as the incident ray for the next total internal reflection. As each time the incidence angle is more than the critical angle at the core cladding.
interface. Therefore the light ray propagates inside the core of The optical fiber with successive total internal reflections.

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Acceptance Angle and Acceptance Cone
Now first we will understand the concept of acceptance cone. You can see this acceptance cone in the image given above. For the total internal reflection to take place
Now you know the concept of acceptance cone. So it is very easy to understand, what is acceptance angle.
Acceptance angle is just the conical half angle of the acceptance cone. This acceptance angle is shown in the diagram here.
As already defined, "Acceptance angle is the maximum angle with the axis of the optical fiber at which light can enter the fiber, in order to be propagated through it".
The light rays that are outside this acceptance cone are not accepted by the optical fiber, that's why it is known as acceptance cone.

Numerical Aperture (NA)
Numerical aperture in case of optical fiber communication can be defined as- "The light gathering (collecting) capacity of an optical fibre".

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