Question

Find the minimum angle${\mathbf{\theta }}_{\mathbf{i}}$for total reflection in the optical fiber in Figure 20-21 if the index of refraction of the cladding is 1.400 and the index of refraction of the core is

(a) 1.600 or

(b) 1.800.

Short answer

1. The entire reflection in an optical fibre, the minimum angle ${\mathrm{\theta }}_{\mathrm{i}}$for 1.600is $\mathrm{\theta i}\ge 61.04°$
2. The entire reflection in an optical fibre, the minimum angle ${\mathrm{\theta }}_{\mathrm{i}}$ for 1.800is $\mathrm{\theta i}\ge 51.06°$

Step-by-step solution

Definition of optical fiber

• Fiber optics, often known as optical fibre, is a technology that uses light pulses to convey data along a glass or plastic fibre.
• A fibre optic cable can have anywhere from a few to several hundred of these glass fibres.
• The glass fibre core is surrounded by another glass layer called cladding.

Determine the minimum angle θi  for total reflection in the optical fiber in 1.600

(a)

For entire reflection, the minimal angle ${\mathrm{\theta }}_{\mathrm{i}}$is

${\mathrm{sin\theta }}_{\mathrm{i}}=\frac{{\mathrm{n}}_{\mathrm{cladding}}}{{\mathrm{n}}_{\mathrm{core}}}$

Simplify fortheminimum angle${\mathrm{\theta }}_{\mathrm{i}}$for total reflection in the optical fiber in 1.600.

For${\mathrm{n}}_{\mathrm{core}}=1.6$,the${\mathrm{\theta }}_{\mathrm{i}}$is:

$$\begin{gathered} {\mathrm{sin\theta }}_{\mathrm{i}}=\frac{1.4}{1.6} \\ {\mathrm{sin\theta }}_{\mathrm{i}}=0.875 \\ {\mathrm{\theta }}_{\mathrm{i}}=61.04° \end{gathered}$$

The entire reflection in an optical fibre, the minimum angle ${\mathrm{\theta }}_{\mathrm{i}}$is $\mathrm{\theta i}\ge 61.04°$

Determine the minimum angle θi  for total reflection in the optical fiber in 1.800

(b)

Simplify forthe minimum angle ${\mathrm{\theta }}_{\mathrm{i}}$for total reflection in the optical fiber in 1.800

For ${\mathrm{n}}_{\mathrm{core}}=1.8$, the ${\mathrm{\theta }}_{\mathrm{i}}$is:

$$\begin{gathered} {\mathrm{sin\theta }}_{\mathrm{i}}=\frac{1.4}{1.8} \\ {\mathrm{sin\theta }}_{\mathrm{i}}=0.778 \\ {\mathrm{\theta }}_{\mathrm{i}}=51.08° \end{gathered}$$

The entire reflection in an optical fibre, the minimum angle ${\mathrm{\theta }}_{\mathrm{i}}$is ${\mathrm{\theta }}_{\mathrm{i}}\ge 51.06°$