Question

A medium has relative permeability $\frac{1}{9}$ and relative permittivity 25. Find critical angle for medium w.r.t. vacuum.

• A. ${53}^{\circ }$
• B. ${37}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is B ${37}^{\circ }$

Assuming $n$ to be refractive index, then
$n=\frac{C}{v}C=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}},v=\frac{1}{\sqrt{\mu ϵ}}$
$n=\frac{C}{v}=\frac{\frac{1}{\sqrt{{\mu }_0{ϵ}_0}}}{\frac{1}{\sqrt{\mu ϵ}}}=\sqrt{\frac{\mu }{{\mu }_o}.\frac{ϵ}{{ϵ}_o}}=\sqrt{\frac{1}{9}\times 25}=\frac{5}{3}$
$sin{\theta }_{critical}=\frac{1}{n}=\frac{3}{5}$
${\theta }_{critical}={37}^o$