What is acceptance angle and numerical aperture?
The correct answer and explanation is :
Correct Answer:
Acceptance angle is the maximum angle at which light can enter the core of an optical fiber and still be guided effectively through total internal reflection.
Numerical Aperture (NA) is a dimensionless number that characterizes the range of angles over which the fiber can accept light. It is given by the formula:
[
\text{NA} = \sqrt{n_1^2 – n_2^2}
]
Where:
- ( n_1 ) = refractive index of the fiber core
- ( n_2 ) = refractive index of the cladding
The acceptance angle ( \theta_a ) is related to the numerical aperture by:
[
\sin(\theta_a) = \text{NA}
]
300 Words Explanation:
In optical fiber communication, light must be efficiently coupled into the fiber core for effective transmission. Two key parameters that describe how much light an optical fiber can accept are the acceptance angle and numerical aperture (NA).
The acceptance angle is the maximum angle at which light rays can strike the fiber core’s end face and still be guided through the fiber via total internal reflection. Light entering the fiber within this angle will travel down the core by reflecting at the core-cladding boundary. If the angle exceeds this limit, the light will refract into the cladding and be lost.
Numerical aperture (NA) quantifies this light-accepting ability of the fiber. It is a dimensionless measure derived from the refractive indices of the core and cladding. A higher NA means the fiber can accept light from a wider range of angles, which is particularly useful when coupling light from a source such as an LED or laser.
For example, if the core refractive index is 1.48 and the cladding is 1.46, then:
[
\text{NA} = \sqrt{1.48^2 – 1.46^2} \approx 0.242
]
This implies:
[
\theta_a = \sin^{-1}(0.242) \approx 14^\circ
]
Thus, light entering at angles up to 14° relative to the fiber axis will be guided.
Understanding NA and acceptance angle is crucial in fiber optics because they directly impact how efficiently light from a source is coupled into the fiber and how the system performs over distances.
