Question

Refer figure, core has refractive index ${\mu }_1=1.424$. The cladding refractive index ${\mu }_2=1.39$. In such a case, will the light beam propagate?

• A. Yes
• B. No
• C. Data given is insufficient to decide
• D. The beam propagation is not affected with refractive indices of fibre core and cladding

Answer 1

Answer: (A)

If ${\mu }_1$ is the refractive index of core of optical fibre, then
${\mu }_1=\frac{sin10^{\circ }}{sin{7}^{\circ }}=\frac{0.1736}{0.1219}=1.424$
Critical angle at core and cladding surface is
$sinC=\frac{{\mu }_2}{{\mu }_1}=\frac{1.39}{1.424}=0.9761=sin77^{\circ }27^{\prime }$
$C=77^{\circ }27^{\prime }$
The angle of incidence on core-cladding surface $=90^{\circ }-7^{\circ }=83^{\circ }$, which is greater than critical angle, hence beam will propagate through optical fibre.