Two optical fibres are connected through a connector to form an i
Two optical fibres are connected through a connector to form an interface as shown. If the wave is travelling from medium 1 to medium 2 then the reflection and transmission coefficients are respectively.
[Assume both fibers as low loss dielectrics]
A. 0.101, 1.101
B. 1.101, 0.101
C. -0.101, 0.899
D. 0.899, -0.101
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Concept:
Reflection coefficient \(\text{ }\!\!\Gamma\!\!\text{ }=\frac{{{\eta }_{2}}-{{\eta }_{1}}}{{{\eta }_{2}}+{{\eta }_{1}}}\)
Transmission coefficient \(=\frac{2{{\eta }_{2}}}{{{\eta }_{1}}+{{\eta }_{2}}}=1+\text{ }\!\!\Gamma\!\!\text{ }\)
Where η = intrinsic impedance \(=\sqrt{\frac{\mu }{\epsilon }}\)
Calculations:
\({{\eta }_{2}}=\sqrt{\frac{{{\mu }_{2}}}{{{\epsilon }_{2}}}}=\sqrt{\frac{1}{4}}\)
\({{\eta }_{1}}=\sqrt{\frac{{{\mu }_{1}}}{{{\epsilon }_{1}}}}=\sqrt{\frac{1}{6}}\)
\(\text{ }\!\!\Gamma\!\!\text{ }=\frac{\frac{1}{\sqrt{4}}-\frac{1}{\sqrt{6}}}{\frac{1}{\sqrt{6}}+\frac{1}{4}}=\frac{0.50-0.408}{0.50+0.408}\)
= 0.101
T = 1 + Γ
= 1 + 0.101
= 1.101