Question

A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index $\mu =1.5$) making an incidence angle of ${60}^{\circ }$ on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to traverse the straight fiber of length 1 km

• A. $3.33\mu sec$
• B. $6.67\mu sec$
• C. $5.77\mu sec$
• D. $3.85\mu sec$

Answer 1

The correct option is D $3.85\mu sec$

When total internal reflection just takes place from lateral surface then i = C i.e.= ${60}^{\circ }$
From $\mu =\frac{1}{sinC}\Rightarrow \mu =\frac{2}{\sqrt{3}}$
Hence time taken by light traverse some distance in medium $t=\frac{\mu x}{C}$
$\Rightarrow t=\frac{\frac{2}{\sqrt{3}}\times (1\times {10}^3)}{3\times {10}^8}=3.85\mu sec.$