Q21Engineering Physics

Question

Answer 1

The Acceptance Angle ( $θ_{a}$ ) mathematically represents the absolute maximum half-angle of the highly specific cone of light that can physically enter the fiber and successfully undergo Total Internal Reflection (TIR) entirely within the core.

Given Optical Parameters

Core Refractive Index ( $μ_{1}$ ): $1.62$
Cladding Refractive Index ( $μ_{2}$ ): $1.52$
External Medium (Water) Refractive Index ( $μ_{0}$ ): $1.33$

Step 1: Calculating the Numerical Aperture (NA)

The fundamental Numerical Aperture rigidly defines the innate light-gathering ability of the specific optical fiber, determined entirely by its internal materials:

N A = μ_{1}^{2} - μ_{2}^{2}

N A = (1.62)^{2} - (1.52)^{2} = 2.6244 - 2.3104 = 0.3140 \approx 0.5604

Step 2: Calculating the Acceptance Angle in Water

The relationship strictly connecting the external acceptance angle directly to the internal NA is rigorously derived from Snell's law applied directly at the external entrance interface:

μ_{0} sin θ_{a} = N A

sin θ_{a} = \frac{N A}{μ _{0}} = \frac{0.5604}{1.33} \approx 0.4213

Solving strictly for the angle:

θ_{a} = arcsin (0.4213) \approx 24.9 1^{\circ}

Q21Engineering Physics

Question

Answer

Given Optical Parameters

Step 1: Calculating the Numerical Aperture (NA)

Step 2: Calculating the Acceptance Angle in Water